From Sat Jan 15 13:16:54 2005 Date: Sat, 15 Jan 2005 13:16:54 -0600 (CST) From: Postmaster Subject: Message from mail server Content-Length: 94 Mime-Version: 1.0 Status: RO X-IMAP: 1105816614 36 Delete. This is a system message. --END+PSEUDO-- From owner-reliable_computing [at] interval [dot] louisiana.edu Sun Jan 2 17:08:15 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j02N8EKT000189 for ; Sun, 2 Jan 2005 17:08:14 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j02N8E64000188 for reliable_computing-outgoing; Sun, 2 Jan 2005 17:08:14 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j02N86Ze000183 for ; Sun, 2 Jan 2005 17:08:11 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j02N6qF04005 for ; Sun, 2 Jan 2005 16:06:52 -0700 (MST) Message-Id: <200501022306.j02N6qF04005 [at] cs [dot] utep.edu> Date: Sun, 2 Jan 2005 16:06:52 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: from NA Digest To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: pNtSqaHDH9YKjp9cs+jphw== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: RO X-Status: $$$$ X-UID: 0000000001 From: Go05 Date: Tue, 28 Dec 2004 10:06:18 +0100 (CET) Subject: Workshop in Spain on Global Optimization Dear colleagues, Happy new year on behalf of the organising committee of the INTERNATIONAL WORKSHOP ON GLOBAL OPTIMIZATION GO05, Almeria, Spain Before you start making new plans for 2005, let us remind you of the workshop. We have been arranging facilities in the pitoresque village of San Jose, which makes it possible to keep the fee low and being in a beautiful and calm environment. Timing: 18th-22th September 2005 Participants arrive on Saturday 17 and leave Thursday 22, afternoon. Global schedule: Deadline for the submission of abstracts May 15th, 2005 Notification of acceptance June 15th, 2005 Deadline for early registration (reduced fee) June 30th, 2005 Deadline for last minute registration (450) July 28th, 2005 On-site reception September 17th, 2005 Start of conference September 18th, 2005 Publication: Two special issues of the Journal of Global Optimization will publish papers emerging from the talks after the regular refereeing procedure. Organising committee: Emilio Carrizosa, Sevilla Tibor Csendes, Szeged Inmaculada Garcia, Almeria Eligius Hendrix, Wageningen Panos Pardalos, Florida Local organisers: Miguel Cobo Leocadio Casado Pilar Ortigosa Boglarka Toth Consolacion Gil Raul Banos Juana Redondo Keep updated via http://dali.ace.ual.es/~go05/ ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Jan 3 08:36:51 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03EapPM001883 for ; Mon, 3 Jan 2005 08:36:51 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j03Eaoqm001882 for reliable_computing-outgoing; Mon, 3 Jan 2005 08:36:50 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03EagTH001878 for ; Mon, 3 Jan 2005 08:36:48 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j03EZPL07429; Mon, 3 Jan 2005 07:35:25 -0700 (MST) Message-Id: <200501031435.j03EZPL07429 [at] cs [dot] utep.edu> Date: Mon, 3 Jan 2005 07:35:24 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: SciCADE To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu Cc: krj [at] cs [dot] toronto.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: 0LIeaxMGDhDyeY1Einrt8A== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000002 ------------- Begin Forwarded Message ------------- From: krj [at] cs [dot] toronto.edu ... there would be two sessions on Validated methods for differential equations at the upcoming SciCADE meeting in Nagoya, Japan, May 23-27, 2005. The URL for the conference is http://www.math.human.nagoya-u.ac.jp/scicade05/ ... The focus of the conference is not validated computing, but there will be two sessions on validated methods for differential equations. However, it is a very good conference for anyone interested in numerical methods for differential equations. Best regards, Ken ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Jan 3 13:10:31 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03JAVpG002311 for ; Mon, 3 Jan 2005 13:10:31 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j03JAU80002310 for reliable_computing-outgoing; Mon, 3 Jan 2005 13:10:30 -0600 (CST) Received: from imap.univie.ac.at (mail.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03JALOA002306 for ; Mon, 3 Jan 2005 13:10:27 -0600 (CST) Received: from univie.ac.at (theseus.mat.univie.ac.at [131.130.16.23]) by imap.univie.ac.at (8.12.10/8.12.10) with ESMTP id j03J8xFb138470; Mon, 3 Jan 2005 20:09:01 +0100 Message-ID: <41D9984B.3070901 [at] univie [dot] ac.at> Date: Mon, 03 Jan 2005 20:08:59 +0100 From: Arnold Neumaier Organization: University of Vienna User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.4.3) Gecko/20041005 X-Accept-Language: en, de MIME-Version: 1.0 To: interval Subject: quadratic equation with interval coefficients Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-DCC-ZID-Univie-Metrics: mx8 4249; Body=2 Fuz1=2 Fuz2=2 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000003 Is there a complete discussion in the literature of the solution of a single quadratic equation in one variable, with interval coefficients? Perhaps even an implementation that computes a correctly rounded enclosure for the solution set? I worked out a solution myself, but this problem is so natural that it was probably treated before. Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Jan 3 13:46:13 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03JkC6V002455 for ; Mon, 3 Jan 2005 13:46:13 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j03JkCTT002454 for reliable_computing-outgoing; Mon, 3 Jan 2005 13:46:12 -0600 (CST) Received: from marnier.ucs.louisiana.edu (root [at] marnier [dot] ucs.louisiana.edu [130.70.132.233]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03Jk4DD002450 for ; Mon, 3 Jan 2005 13:46:09 -0600 (CST) Received: from Liberty (h158065.louisiana.edu [130.70.158.65]) by marnier.ucs.louisiana.edu (8.13.1/8.13.1/ull-ucs-mx-host_1.9) with SMTP id j03JimtS019113; Mon, 3 Jan 2005 13:44:53 -0600 (CST) Message-Id: <2.2.32.20050103194652.009da2ac [at] pop [dot] louisiana.edu> X-Sender: rbk5287 [at] pop [dot] louisiana.edu X-Mailer: Windows Eudora Pro Version 2.2 (32) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Mon, 03 Jan 2005 13:46:52 -0600 To: Arnold Neumaier , interval From: "R. Baker Kearfott" Subject: Re: quadratic equation with interval coefficients Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000004 Arnold, I looked at it some years ago, when I was programming the elementary functions for GlobSol's constraint propagation. I even wrote a routine for it. However, I never published it, and it is not contained in the distribution version of GlobSol. Furthermore, I don't think I proved that it was the tightest possible machine enclosure for the solution set. Thus, if I'm the only one who did it, it's "fair game" for you to write it up :-) Best regards, Baker At 08:08 PM 1/3/2005 +0100, Arnold Neumaier wrote: >Is there a complete discussion in the literature of the solution >of a single quadratic equation in one variable, >with interval coefficients? Perhaps even an implementation >that computes a correctly rounded enclosure for the solution set? > >I worked out a solution myself, but this problem is so natural >that it was probably treated before. > > >Arnold Neumaier > > > --------------------------------------------------------------- R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax) (337) 482-5270 (work) (337) 993-1827 (home) URL: http://interval.louisiana.edu/kearfott.html Department of Mathematics, University of Louisiana at Lafayette (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) Box 4-1010, Lafayette, LA 70504-1010, USA --------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Jan 3 14:27:22 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03KRLhY002584 for ; Mon, 3 Jan 2005 14:27:21 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j03KRLQk002583 for reliable_computing-outgoing; Mon, 3 Jan 2005 14:27:21 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03KRDUO002579 for ; Mon, 3 Jan 2005 14:27:18 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j03KMoN09441; Mon, 3 Jan 2005 13:22:50 -0700 (MST) Message-Id: <200501032022.j03KMoN09441 [at] cs [dot] utep.edu> Date: Mon, 3 Jan 2005 13:22:50 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: quadratic equation with interval coefficients To: Arnold.Neumaier [at] univie [dot] ac.at, reliable_computing [at] interval [dot] louisiana.edu, rbk [at] louisiana [dot] edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: frxjkwOM9tB+iCVUyDGcbw== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000005 It is described in the paper E. R. Hansen and G. W. Walster, Sharp bounds on interval polynomial roots, Reliable Computing, 2002, Vol. 8, No. 2, pp. 115-122. This is how it works for the example that was sent to the list: From vladik Mon Dec 27 22:52:10 2004 Date: Mon, 27 Dec 2004 22:52:10 -0700 (MST) From: Vladik Kreinovich Subject: Re: requing solution To: mailtomallik [at] yahoo [dot] com X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Mime-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: nump1OwkSUwq4CkUCN76kg== Content-Length: 2283 Status: O X-Status: $$$$ X-UID: 0000000006 Dear Collegue, If I understand you correctly, you want to find the range of all the values x for which ax^2+bx+c=0 for some a in [1,2], b in [2,3], and c in [3,4]. For any given x, this condition is equivalent to the fact that 0 belongs to the range of ax^2+bx+c when a in [1,2], b in [2,3], and c in [3,4]. Since the dependence of ax^2+bx+c on a, b, anc is monotonic, this range can be explicitly computed. For x>=0, the range is [x^2+2x+3,2x^2+3x+4]. For each of these quadratic bounds, we can explicitly find the roots and thus, describe the ranges where this bound is negative and positive. Roots of an interval polynomial correspond to the case when the lower bound is non-positive and the upper bound is non-negative. For these particular bounds, both are always positive for x>=0, so there are no positive roots of the interval polynomial. For x<0, the range is [x^2+3x+2,2x^2+2x+4]. Same thing. The first function has roots at x=-2 and x=-1, so it is non-positive for -2<= x<= -1. The second is always non-negative. So, the set of possible roots of the original interval polynomial are [-2,-1]. Vladik > X-Sender: rbk5287 [at] pop [dot] louisiana.edu > Mime-Version: 1.0 > Date: Mon, 03 Jan 2005 13:46:52 -0600 > To: Arnold Neumaier , interval > From: "R. Baker Kearfott" > Subject: Re: quadratic equation with interval coefficients > > Arnold, > > I looked at it some years ago, when I was programming the elementary > functions for GlobSol's constraint propagation. I even wrote a routine > for it. However, I never published it, and it is not contained > in the distribution version of GlobSol. Furthermore, I don't think > I proved that it was the tightest possible machine enclosure for the > solution set. Thus, if I'm the only one who did it, it's "fair game" > for you to write it up :-) > > Best regards, > > Baker > > At 08:08 PM 1/3/2005 +0100, Arnold Neumaier wrote: > >Is there a complete discussion in the literature of the solution > >of a single quadratic equation in one variable, > >with interval coefficients? Perhaps even an implementation > >that computes a correctly rounded enclosure for the solution set? > > > >I worked out a solution myself, but this problem is so natural > >that it was probably treated before. > > > > > >Arnold Neumaier > > > > > > > > --------------------------------------------------------------- > R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax) > (337) 482-5270 (work) (337) 993-1827 (home) > URL: http://interval.louisiana.edu/kearfott.html > Department of Mathematics, University of Louisiana at Lafayette > (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) > Box 4-1010, Lafayette, LA 70504-1010, USA > --------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Jan 3 15:40:53 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03Ler4o002741 for ; Mon, 3 Jan 2005 15:40:53 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j03Leq8t002740 for reliable_computing-outgoing; Mon, 3 Jan 2005 15:40:52 -0600 (CST) Received: from imap.univie.ac.at (mail.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03LehlN002736 for ; Mon, 3 Jan 2005 15:40:49 -0600 (CST) Received: from univie.ac.at (theseus.mat.univie.ac.at [131.130.16.23]) by imap.univie.ac.at (8.12.10/8.12.10) with ESMTP id j03LcrFb502844; Mon, 3 Jan 2005 22:39:01 +0100 Message-ID: <41D9BB6D.3000203 [at] univie [dot] ac.at> Date: Mon, 03 Jan 2005 22:38:53 +0100 From: Arnold Neumaier Organization: University of Vienna User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.4.3) Gecko/20041005 X-Accept-Language: en, de MIME-Version: 1.0 To: Vladik Kreinovich CC: reliable_computing [at] interval [dot] louisiana.edu, rbk [at] louisiana [dot] edu Subject: Re: quadratic equation with interval coefficients References: <200501032022.j03KMoN09441 [at] cs [dot] utep.edu> In-Reply-To: <200501032022.j03KMoN09441 [at] cs [dot] utep.edu> Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-DCC-ZID-Univie-Metrics: mx8 4248; Body=4 Fuz1=4 Fuz2=4 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000007 Vladik Kreinovich wrote: > It is described in the paper E. R. Hansen and G. W. Walster, Sharp bounds on > interval polynomial roots, Reliable Computing, 2002, Vol. 8, No. 2, pp. > 115-122. Thanks. I hope they didn't patent it! Arnold From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Jan 3 21:09:39 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0439d0e003249 for ; Mon, 3 Jan 2005 21:09:39 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0439d2Q003248 for reliable_computing-outgoing; Mon, 3 Jan 2005 21:09:39 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0439Ut9003244 for ; Mon, 3 Jan 2005 21:09:36 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j0438Be12134 for ; Mon, 3 Jan 2005 20:08:11 -0700 (MST) Message-Id: <200501040308.j0438Be12134 [at] cs [dot] utep.edu> Date: Mon, 3 Jan 2005 20:08:12 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: quadratic equation with interval coefficients To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: Q6QSwTlKNdnvK7Y7DPaE5Q== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000008 FYI. Vladik ------------- Begin Forwarded Message ------------- From: "G. William Walster" ... the algorithm is also contained in Chapter 8 of the second edition of "Global Optimization Using Interval Analysis." ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Jan 3 21:35:58 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j043Zwue003418 for ; Mon, 3 Jan 2005 21:35:58 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j043ZwKm003417 for reliable_computing-outgoing; Mon, 3 Jan 2005 21:35:58 -0600 (CST) Received: from its-exsmtp1.marqnet.mu.edu (email.marquette.edu [134.48.20.169]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j043Znu0003413 for ; Mon, 3 Jan 2005 21:35:55 -0600 (CST) Received: from its-exfe1.marqnet.mu.edu ([134.48.20.165]) by its-exsmtp1.marqnet.mu.edu with Microsoft SMTPSVC(6.0.3790.211); Mon, 3 Jan 2005 21:37:37 -0600 Received: from [192.168.1.103] ([134.48.233.103] RDNS failed) by its-exfe1.marqnet.mu.edu with Microsoft SMTPSVC(6.0.3790.211); Mon, 3 Jan 2005 21:37:33 -0600 User-Agent: Microsoft-Entourage/10.1.4.030702.0 Date: Mon, 03 Jan 2005 21:35:59 -0600 Subject: Re: quadratic equation with interval coefficients From: George Corliss To: Arnold Neumaier , Vladik Kreinovich CC: , Message-ID: In-Reply-To: <41D9BB6D.3000203 [at] univie [dot] ac.at> Mime-version: 1.0 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit X-OriginalArrivalTime: 04 Jan 2005 03:37:33.0541 (UTC) FILETIME=[B9E40950:01C4F20E] Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000009 Arnold and all, >> It is described in the paper E. R. Hansen and G. W. Walster, Sharp bounds on >> interval polynomial roots, Reliable Computing, 2002, Vol. 8, No. 2, pp. >> 115-122. > > Thanks. I hope they didn't patent it! They have applied for one. Patent application number: 20030055857 Method and apparatus for computing roots of a polynomial equation with interval coefficients You may view the application at http://appft1.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&u=%2Fneta html%2FPTO%2Fsearch-adv.html&r=16&p=1&f=G&l=50&d=PG01&S1=walster.IN.&OS=IN/w alster&RS=IN/walster Of the applications Bill has submitted, 8 patents have been issued. See http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&u=%2Fnetah tml%2Fsearch-adv.htm&r=0&p=1&f=S&l=50&Query=IN%2Fwalster&d=ptxt Dr. George F. Corliss Electrical and Computer Engineering Marquette University PO Box 1881 1515 W. Wisconsin Ave. Milwaukee WI 53201-1881 USA 414-288-6599; Fax: 288-5579; Dept. 288-6280 George.Corliss [at] Marquette [dot] edu From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Jan 4 01:12:39 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j047Cduh003822 for ; Tue, 4 Jan 2005 01:12:39 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j047CcwN003821 for reliable_computing-outgoing; Tue, 4 Jan 2005 01:12:38 -0600 (CST) Received: from poczta.polsl.pl (castor.polsl.pl [157.158.3.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j047CS2m003817 for ; Tue, 4 Jan 2005 01:12:34 -0600 (CST) Received: from pownuk ([193.25.187.160]) by poczta.polsl.pl with Microsoft SMTPSVC(6.0.3790.211); Tue, 4 Jan 2005 08:10:22 +0100 From: "Andrzej Pownuk" To: Subject: RE: quadratic equation with interval coefficients Date: Tue, 4 Jan 2005 08:11:27 +0100 Message-ID: X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook, Build 10.0.6626 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 In-Reply-To: Importance: Normal X-OriginalArrivalTime: 04 Jan 2005 07:10:22.0687 (UTC) FILETIME=[74E516F0:01C4F22C] Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000010 Dear George, According to my knowledge, these patents are not valid (at least) in Europe. Art. 52 (EUROPEAN PATENT CONVENTION) says that: (a) discoveries, scientific theories and mathematical methods; (b) aesthetic creations; (c) schemes, rules and methods for performing mental acts, playing games or doing business, and programs for computers; (d) presentations of information. cannot be patentable http://www.european-patent-office.org/legal/epc/e/ar52.html This law is still valid. http://www.gnu.org/thankpoland.html Then at this moment these patents are problems for people living in the USA. I am not a lawyer. Correct me if I am wrong. Regards, Andrzej Pownuk --------------------------------------------- Ph.D., research associate at: Chair of Theoretical Mechanics Faculty of Civil Engineering Silesian University of Technology ul. Krzywoustego 7 44-100 Gliwice, Poland Tel/fax: 0048 32 2371542 Mobile: 0048 606 550147 URL: http://zeus.polsl.gliwice.pl/~pownuk E-mail: Andrzej.Pownuk [at] polsl [dot] pl --------------------------------------------- > Arnold and all, > > >> It is described in the paper E. R. Hansen and G. W. Walster, Sharp > bounds on > >> interval polynomial roots, Reliable Computing, 2002, Vol. 8, No. 2, pp. > >> 115-122. > > > > Thanks. I hope they didn't patent it! > > They have applied for one. Patent application number: 20030055857 > Method and apparatus for computing roots of a polynomial equation with > interval coefficients > > You may view the application at > http://appft1.uspto.gov/netacgi/nph- > Parser?Sect1=PTO2&Sect2=HITOFF&u=%2Fneta > html%2FPTO%2Fsearch- > adv.html&r=16&p=1&f=G&l=50&d=PG01&S1=walster.IN.&OS=IN/w > alster&RS=IN/walster > > > Of the applications Bill has submitted, 8 patents have been issued. See > http://patft.uspto.gov/netacgi/nph- > Parser?Sect1=PTO2&Sect2=HITOFF&u=%2Fnetah > tml%2Fsearch-adv.htm&r=0&p=1&f=S&l=50&Query=IN%2Fwalster&d=ptxt > > Dr. George F. Corliss > Electrical and Computer Engineering > Marquette University > PO Box 1881 > 1515 W. Wisconsin Ave. > Milwaukee WI 53201-1881 USA > 414-288-6599; Fax: 288-5579; Dept. 288-6280 > George.Corliss [at] Marquette [dot] edu > From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Jan 4 05:18:05 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04BI47v004615 for ; Tue, 4 Jan 2005 05:18:05 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j04BI4vY004614 for reliable_computing-outgoing; Tue, 4 Jan 2005 05:18:04 -0600 (CST) Received: from interferon.mpi-sb.mpg.de (mail.mpi-sb.mpg.de [139.19.1.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04BHtd3004610 for ; Tue, 4 Jan 2005 05:18:01 -0600 (CST) Received: from amavis by interferon.mpi-sb.mpg.de with scanned-ok (Exim 3.36 #1 (Debian)) id 1Clmg1-0005j8-00 for ; Tue, 04 Jan 2005 12:16:37 +0100 Received: from mpino2303.ag2.mpi-sb.mpg.de ([139.19.24.75]) by interferon.mpi-sb.mpg.de with esmtp (Exim 3.36 #1 (Debian)) id 1Clmfz-0005bD-00; Tue, 04 Jan 2005 12:16:35 +0100 Subject: Re: quadratic equation with interval coefficients From: Stefan Ratschan To: reliable_computing [at] interval [dot] louisiana.edu In-Reply-To: <200501032022.j03KMoN09441 [at] cs [dot] utep.edu> References: <200501032022.j03KMoN09441 [at] cs [dot] utep.edu> Content-Type: text/plain Message-Id: <1104837365.3358.8.camel@localhost> Mime-Version: 1.0 X-Mailer: Ximian Evolution 1.4.6 Date: Tue, 04 Jan 2005 12:16:05 +0100 Content-Transfer-Encoding: 7bit X-Virus-Scanned: by AMaViS perl-11 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000011 On Mon, 2005-01-03 at 21:22, Vladik Kreinovich wrote: > It is described in the paper E. R. Hansen and G. W. Walster, Sharp bounds on > interval polynomial roots, Reliable Computing, 2002, Vol. 8, No. 2, pp. > 115-122. To me it seems that this method is a reinvention of what already appears in Section 7 of @Article{Hong:94b, author = "Hoon Hong and Volker Stahl", title = "Safe Starting Regions by Fixed Points and Tightening", journal = "Computing", year = 1994, volume = 53, pages = "323--335", } ... this might also be relevant for the patent application ... Stefan Ratschan From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Jan 4 08:36:28 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04EaShE004973 for ; Tue, 4 Jan 2005 08:36:28 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j04EaSXB004972 for reliable_computing-outgoing; Tue, 4 Jan 2005 08:36:28 -0600 (CST) Received: from marnier.ucs.louisiana.edu (root [at] marnier [dot] ucs.louisiana.edu [130.70.132.233]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04EaJCW004968 for ; Tue, 4 Jan 2005 08:36:24 -0600 (CST) Received: from Liberty (h158065.louisiana.edu [130.70.158.65]) by marnier.ucs.louisiana.edu (8.13.1/8.13.1/ull-ucs-mx-host_1.9) with SMTP id j04EZ0MF007820; Tue, 4 Jan 2005 08:35:05 -0600 (CST) Message-Id: <2.2.32.20050104143301.009ec908 [at] pop [dot] louisiana.edu> X-Sender: rbk5287 [at] pop [dot] louisiana.edu X-Mailer: Windows Eudora Pro Version 2.2 (32) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Tue, 04 Jan 2005 08:33:01 -0600 To: "r. corless" , George Corliss From: "R. Baker Kearfott" Subject: Re: quadratic equation with interval coefficients Cc: Arnold Neumaier , Vladik Kreinovich , reliable_computing [at] interval [dot] louisiana.edu Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000012 Hmmm.... let me play devil's advocate: It brings up an interesting question of standards for original work for publication. Presumably computing the roots of interval polynomials was previously published as a research publication. An algorithm or procedure might possibly be derivable by any of us; nonetheless, a clear, readable written record of it could still be valuable to all, and writing it down in a clear and understandable way may take some effort. So, although it may not be surprising and although any of a number of us might have been able to derive it in a fairly straightforward way, might the written record still be valuable to the community as a whole? Best regards, Baker At 09:12 AM 1/4/2005 -0500, r. corless wrote: > >Interesting. I was speaking to an intellectual-property lawyer last week >(he will marry my sister-in-law in July, this is just family, I am not >applying for patents myself :-) and he pointed out to me that the >"hard" question for patents is not "originality" but "obviousness". A >patent will not be granted for something that is "obvious" to someone >"skilled in the art". > >I understand that phrase "skilled in the art" to mean an ordinarily >competent interval practitioner in this case, and not to someone elite >(and it is clear that there are elite practitioners on this mailing list, >to be sure). > >So, here's the question for the community: Is the solution of >interval polynomials "obvious", given competent knowledge of interval >arithmetic? > >Would you set it on an exam? > >-r > > > >On Mon, 3 Jan 2005, George Corliss wrote: > >> Arnold and all, >> >> >> It is described in the paper E. R. Hansen and G. W. Walster, Sharp bounds on >> >> interval polynomial roots, Reliable Computing, 2002, Vol. 8, No. 2, pp. >> >> 115-122. >> > >> > Thanks. I hope they didn't patent it! >> >> They have applied for one. Patent application number: 20030055857 >> Method and apparatus for computing roots of a polynomial equation with >> interval coefficients >> >> You may view the application at >> http://appft1.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&u=%2Fneta >> html%2FPTO%2Fsearch-adv.html&r=16&p=1&f=G&l=50&d=PG01&S1=walster.IN.&OS=IN/w >> alster&RS=IN/walster >> >> >> Of the applications Bill has submitted, 8 patents have been issued. See >> http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&u=%2Fnetah >> tml%2Fsearch-adv.htm&r=0&p=1&f=S&l=50&Query=IN%2Fwalster&d=ptxt >> >> Dr. George F. Corliss >> Electrical and Computer Engineering >> Marquette University >> PO Box 1881 >> 1515 W. Wisconsin Ave. >> Milwaukee WI 53201-1881 USA >> 414-288-6599; Fax: 288-5579; Dept. 288-6280 >> George.Corliss [at] Marquette [dot] edu >> >> >> > > --------------------------------------------------------------- R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax) (337) 482-5270 (work) (337) 993-1827 (home) URL: http://interval.louisiana.edu/kearfott.html Department of Mathematics, University of Louisiana at Lafayette (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) Box 4-1010, Lafayette, LA 70504-1010, USA --------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Jan 4 09:06:19 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04F6Jlb005108 for ; Tue, 4 Jan 2005 09:06:19 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j04F6Jia005107 for reliable_computing-outgoing; Tue, 4 Jan 2005 09:06:19 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04F6GWd005103 for ; Tue, 4 Jan 2005 09:06:16 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j04F6GEa005102 for reliable_computing [at] interval [dot] louisiana.edu; Tue, 4 Jan 2005 09:06:16 -0600 (CST) Received: from relay0.EECS.Berkeley.EDU (relay0.EECS.Berkeley.EDU [169.229.60.163]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03JahD0002434 for ; Mon, 3 Jan 2005 13:36:49 -0600 (CST) Received: from gateway2.EECS (gateway2.EECS.Berkeley.EDU [169.229.60.39]) by relay0.EECS.Berkeley.EDU (8.13.2/8.12.10) with ESMTP id j03JZTgN017804; Mon, 3 Jan 2005 11:35:30 -0800 (PST) Received: from cs.berkeley.edu (adsl-66-126-183-181.dsl.snfc21.pacbell.net [66.126.183.181]) by gateway2.EECS.Berkeley.EDU (iPlanet Messaging Server 5.2 Patch 2 (built Jul 14 2004)) with ESMTPSA id <0I9R00KK2AF5LQ [at] gateway2 [dot] EECS.Berkeley.EDU>; Mon, 03 Jan 2005 11:35:29 -0800 (PST) Date: Mon, 03 Jan 2005 11:35:29 -0800 From: James Demmel Subject: Re: quadratic equation with interval coefficients To: Arnold Neumaier Cc: interval Message-id: <41D99E81.BAECEECC [at] cs [dot] berkeley.edu> MIME-version: 1.0 X-Mailer: Mozilla 4.79 [en] (Windows NT 5.0; U) Content-type: text/plain; charset=us-ascii Content-transfer-encoding: 7BIT X-Accept-Language: en References: <41D9984B.3070901 [at] univie [dot] ac.at> Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000013 Yves Nievergelt, ynievergelt [at] ewu [dot] edu, has a paper on a related result. Jim Demmel Arnold Neumaier wrote: > Is there a complete discussion in the literature of the solution > of a single quadratic equation in one variable, > with interval coefficients? Perhaps even an implementation > that computes a correctly rounded enclosure for the solution set? > > I worked out a solution myself, but this problem is so natural > that it was probably treated before. > > Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Jan 4 09:17:28 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04FHSCr005563 for ; Tue, 4 Jan 2005 09:17:28 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j04FHSf0005562 for reliable_computing-outgoing; Tue, 4 Jan 2005 09:17:28 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04FHPI2005558 for ; Tue, 4 Jan 2005 09:17:25 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j04FHPxi005557 for reliable_computing [at] interval [dot] louisiana.edu; Tue, 4 Jan 2005 09:17:25 -0600 (CST) Received: from relay0.EECS.Berkeley.EDU (relay0.EECS.Berkeley.EDU [169.229.60.163]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03JahD0002434 for ; Mon, 3 Jan 2005 13:36:49 -0600 (CST) Received: from gateway2.EECS (gateway2.EECS.Berkeley.EDU [169.229.60.39]) by relay0.EECS.Berkeley.EDU (8.13.2/8.12.10) with ESMTP id j03JZTgN017804; Mon, 3 Jan 2005 11:35:30 -0800 (PST) Received: from cs.berkeley.edu (adsl-66-126-183-181.dsl.snfc21.pacbell.net [66.126.183.181]) by gateway2.EECS.Berkeley.EDU (iPlanet Messaging Server 5.2 Patch 2 (built Jul 14 2004)) with ESMTPSA id <0I9R00KK2AF5LQ [at] gateway2 [dot] EECS.Berkeley.EDU>; Mon, 03 Jan 2005 11:35:29 -0800 (PST) Date: Mon, 03 Jan 2005 11:35:29 -0800 From: James Demmel Subject: Re: quadratic equation with interval coefficients To: Arnold Neumaier Cc: interval Message-id: <41D99E81.BAECEECC [at] cs [dot] berkeley.edu> MIME-version: 1.0 X-Mailer: Mozilla 4.79 [en] (Windows NT 5.0; U) Content-type: text/plain; charset=us-ascii Content-transfer-encoding: 7BIT X-Accept-Language: en References: <41D9984B.3070901 [at] univie [dot] ac.at> Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000014 Yves Nievergelt, ynievergelt [at] ewu [dot] edu, has a paper on a related result. Jim Demmel Arnold Neumaier wrote: > Is there a complete discussion in the literature of the solution > of a single quadratic equation in one variable, > with interval coefficients? Perhaps even an implementation > that computes a correctly rounded enclosure for the solution set? > > I worked out a solution myself, but this problem is so natural > that it was probably treated before. > > Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Jan 4 09:18:51 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04FIokG005628 for ; Tue, 4 Jan 2005 09:18:50 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j04FIoBR005627 for reliable_computing-outgoing; Tue, 4 Jan 2005 09:18:50 -0600 (CST) Received: from marnier.ucs.louisiana.edu (root [at] marnier [dot] ucs.louisiana.edu [130.70.132.233]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04FIgDJ005621 for ; Tue, 4 Jan 2005 09:18:47 -0600 (CST) Received: from Liberty (h158065.louisiana.edu [130.70.158.65]) by marnier.ucs.louisiana.edu (8.13.1/8.13.1/ull-ucs-mx-host_1.9) with SMTP id j04FHN31009489 for ; Tue, 4 Jan 2005 09:17:29 -0600 (CST) Message-Id: <2.2.32.20050104151525.009f9ab8 [at] pop [dot] louisiana.edu> X-Sender: rbk5287 [at] pop [dot] louisiana.edu X-Mailer: Windows Eudora Pro Version 2.2 (32) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Tue, 04 Jan 2005 09:15:25 -0600 To: reliable_computing [at] interval [dot] louisiana.edu From: "R. Baker Kearfott" Subject: Re: quadratic equation with interval coefficients Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000015 Hmmm.... let me play devil's advocate: It brings up an interesting question of standards for original work for publication. Presumably computing the roots of interval polynomials was previously published as a research publication. An algorithm or procedure might possibly be derivable by any of us; nonetheless, a clear, readable written record of it could still be valuable to all, and writing it down in a clear and understandable way may take some effort. So, although it may not be surprising and although any of a number of us might have been able to derive it in a fairly straightforward way, might the written record still be valuable to the community as a whole? Best regards, Baker >At 09:12 AM 1/4/2005 -0500, r. corless wrote: >> >>Interesting. I was speaking to an intellectual-property lawyer last week >>(he will marry my sister-in-law in July, this is just family, I am not >>applying for patents myself :-) and he pointed out to me that the >>"hard" question for patents is not "originality" but "obviousness". A >>patent will not be granted for something that is "obvious" to someone >>"skilled in the art". >> >>I understand that phrase "skilled in the art" to mean an ordinarily >>competent interval practitioner in this case, and not to someone elite >>(and it is clear that there are elite practitioners on this mailing list, >>to be sure). >> >>So, here's the question for the community: Is the solution of >>interval polynomials "obvious", given competent knowledge of interval >>arithmetic? >> >>Would you set it on an exam? >> >>-r >> >> >> >>On Mon, 3 Jan 2005, George Corliss wrote: >> >>> Arnold and all, >>> >>> >> It is described in the paper E. R. Hansen and G. W. Walster, Sharp bounds on >>> >> interval polynomial roots, Reliable Computing, 2002, Vol. 8, No. 2, pp. >>> >> 115-122. >>> > >>> > Thanks. I hope they didn't patent it! >>> >>> They have applied for one. Patent application number: 20030055857 >>> Method and apparatus for computing roots of a polynomial equation with >>> interval coefficients >>> >>> You may view the application at >>> http://appft1.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&u=%2Fneta >>> html%2FPTO%2Fsearch-adv.html&r=16&p=1&f=G&l=50&d=PG01&S1=walster.IN.&OS=IN/w >>> alster&RS=IN/walster >>> >>> >>> Of the applications Bill has submitted, 8 patents have been issued. See >>> http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&u=%2Fnetah >>> tml%2Fsearch-adv.htm&r=0&p=1&f=S&l=50&Query=IN%2Fwalster&d=ptxt >>> >>> Dr. George F. Corliss >>> Electrical and Computer Engineering >>> Marquette University >>> PO Box 1881 >>> 1515 W. Wisconsin Ave. >>> Milwaukee WI 53201-1881 USA >>> 414-288-6599; Fax: 288-5579; Dept. 288-6280 >>> George.Corliss [at] Marquette [dot] edu >>> >>> >>> >> >> > --------------------------------------------------------------- R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax) (337) 482-5270 (work) (337) 993-1827 (home) URL: http://interval.louisiana.edu/kearfott.html Department of Mathematics, University of Louisiana at Lafayette (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) Box 4-1010, Lafayette, LA 70504-1010, USA --------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Jan 4 10:31:06 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04GV6ih005892 for ; Tue, 4 Jan 2005 10:31:06 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j04GV5EW005891 for reliable_computing-outgoing; Tue, 4 Jan 2005 10:31:05 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04GV3rw005887 for ; Tue, 4 Jan 2005 10:31:03 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j04GV3YV005886 for reliable_computing [at] interval [dot] louisiana.edu; Tue, 4 Jan 2005 10:31:03 -0600 (CST) Received: from relay0.EECS.Berkeley.EDU (relay0.EECS.Berkeley.EDU [169.229.60.163]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j03JahD0002434 for ; Mon, 3 Jan 2005 13:36:49 -0600 (CST) Received: from gateway2.EECS (gateway2.EECS.Berkeley.EDU [169.229.60.39]) by relay0.EECS.Berkeley.EDU (8.13.2/8.12.10) with ESMTP id j03JZTgN017804; Mon, 3 Jan 2005 11:35:30 -0800 (PST) Received: from cs.berkeley.edu (adsl-66-126-183-181.dsl.snfc21.pacbell.net [66.126.183.181]) by gateway2.EECS.Berkeley.EDU (iPlanet Messaging Server 5.2 Patch 2 (built Jul 14 2004)) with ESMTPSA id <0I9R00KK2AF5LQ [at] gateway2 [dot] EECS.Berkeley.EDU>; Mon, 03 Jan 2005 11:35:29 -0800 (PST) Date: Mon, 03 Jan 2005 11:35:29 -0800 From: James Demmel Subject: Re: quadratic equation with interval coefficients To: Arnold Neumaier Cc: interval Message-id: <41D99E81.BAECEECC [at] cs [dot] berkeley.edu> MIME-version: 1.0 X-Mailer: Mozilla 4.79 [en] (Windows NT 5.0; U) Content-type: text/plain; charset=us-ascii Content-transfer-encoding: 7BIT X-Accept-Language: en References: <41D9984B.3070901 [at] univie [dot] ac.at> Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000016 Yves Nievergelt, ynievergelt [at] ewu [dot] edu, has a paper on a related result. Jim Demmel Arnold Neumaier wrote: > Is there a complete discussion in the literature of the solution > of a single quadratic equation in one variable, > with interval coefficients? Perhaps even an implementation > that computes a correctly rounded enclosure for the solution set? > > I worked out a solution myself, but this problem is so natural > that it was probably treated before. > > Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Jan 4 14:56:39 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04Kucqx006452 for ; Tue, 4 Jan 2005 14:56:38 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j04Kucpw006451 for reliable_computing-outgoing; Tue, 4 Jan 2005 14:56:38 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04KuYk6006447 for ; Tue, 4 Jan 2005 14:56:34 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j04KuYJR006446 for reliable_computing [at] interval [dot] louisiana.edu; Tue, 4 Jan 2005 14:56:34 -0600 (CST) Received: from lcyoung.math.wisc.edu (lcyoung.math.wisc.edu [144.92.166.90]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j04J1pW1006281 for ; Tue, 4 Jan 2005 13:01:57 -0600 (CST) Received: from erdos.math.wisc.edu (erdos.math.wisc.edu [144.92.166.25]) by lcyoung.math.wisc.edu (8.11.7/8.11.7) with ESMTP id j04IpQv08854; Tue, 4 Jan 2005 12:51:27 -0600 (CST) Date: Tue, 4 Jan 2005 12:51:24 -0600 (CST) From: Hans Schneider To: NETS -- at-net , E-LETTER , Pradeep Misra , Shaun Fallat , "na.digest" , ipnet-digest [at] math [dot] msu.edu, Michael.Unser [at] epfl [dot] ch, SIAGLA-DIGEST , hjt [at] eos [dot] ncsu.edu, SMBnet [at] smb [dot] org, vkm [at] eedsp [dot] gatech.edu, reliable_computing [at] interval [dot] louisiana.edu Subject: LAA contents Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=X-UNKNOWN X-UWMath-MailScanner: Found to be clean Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from QUOTED-PRINTABLE to 8bit by interval.louisiana.edu id j04J1wW1006282 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000017 Linear Algebra and its Applications Volume 396, Pages 1-392 (1 February 2005) 1. Editorial board Pages ii-iii 2. On the solution of Steinâ^À^Ùs equation and Fisherâ^À^Ùs information matrix of an ARMAX process Pages 1-34 André Klein and Peter Spreij 3. Nilpotent linear transformations and the solvability of power-associative nilalgebras Pages 35-53 Ivan Correa, Irvin Roy Hentzel, Pedro Pablo Julca and Luiz Antonio Peresi 4. A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations Pages 55-80 E.K.-W. Chu, H.-Y. Fan and W.-W. Lin 5. On generalized H -matrices Pages 81-90 Ting-Zhu Huang, Shu-Qian Shen and Hou-Biao Li 6. Linear/additive preservers of rank 2 on spaces of alternate matrices over fields Pages 91-102 Xian Zhang 7. On the sensitivity of Lanczos recursions to the spectrum Pages 103-125 Vladimir Druskin, Liliana Borcea and Leonid Knizhnerman 8. Geometry of skew-Hermitian matrices Pages 127-157 Li-Ping Huang and Zhe-Xian Wan 9. Linear maps preserving Drazin inverses of matrices over fields Pages 159-173 Changjiang Bu 10. Some functions reversing the order of positive operators Pages 175-187 Josip PeÄ^ÍariÄ^Ç and Jadranka MiÄ^ÇiÄ^Ç 11. Symmetric triality relations and structurable algebras Pages 189-222 Susumu Okubo 12. On the comparison of some realizability criteria for the real nonnegative inverse eigenvalue problem Pages 223-241 Ricardo Soto, Alberto Borobia and Julio Moro 13. The exponent and circumdiameter of primitive digraphs Pages 243-258 L.F. Dame, D.D. Olesky and P. van den Driessche 14. A Perron Theorem for positive componentwise bilinear maps Pages 259-272 Joseph E. Carroll, Timothy Lauck and Roland H. Lamberson 15. On sensitivity of eigenvalues and eigendecompositions of matrices Pages 273-301 R. Alam and S. Bora 16. Combinatorial designs with two singular values II. Partial geometric designs Pages 303-316 E.R. van Dam and E. Spence 17. A pathway to matrix-variate gamma and normal densities Pages 317-328 A.M. Mathai 18. Convex invertible sets and matrix sign function Pages 329-352 Izchak Lewkowicz, Leiba Rodman and Elad J. Yarkoni 19. Convergence of logarithmic trace inequalities via generalized Lieâ^À^ÓTrotter formulae Pages 353-372 Takayuki Furuta 20. The geometric mean decomposition Pages 373-384 Yi Jiang, William W. Hager and Jian Li 21. The structure of alternating-Hamiltonian matrices Pages 385-390 William C. Waterhouse 22. Author index Pages 391-392 Subscribers to LAA or ScenceDirect may access every paper of LAA published since volume 1 (1968) and also papers now in press, see www.sciencedirect.com . From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 5 05:52:16 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j05BqGDX001573 for ; Wed, 5 Jan 2005 05:52:16 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j05BqFnD001572 for reliable_computing-outgoing; Wed, 5 Jan 2005 05:52:15 -0600 (CST) Received: from imap.univie.ac.at (mailbox-lmtp.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j05Bq5Bi001568 for ; Wed, 5 Jan 2005 05:52:11 -0600 (CST) Received: from univie.ac.at (theseus.mat.univie.ac.at [131.130.16.23]) by imap.univie.ac.at (8.12.10/8.12.10) with ESMTP id j05Bpb0W524472; Wed, 5 Jan 2005 12:51:40 +0100 Message-ID: <41DBD4C9.70406 [at] univie [dot] ac.at> Date: Wed, 05 Jan 2005 12:51:37 +0100 From: Arnold Neumaier Organization: University of Vienna User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.4.3) Gecko/20041005 X-Accept-Language: en, de MIME-Version: 1.0 To: George Corliss CC: Vladik Kreinovich , reliable_computing [at] interval [dot] louisiana.edu, rbk [at] louisiana [dot] edu Subject: Re: quadratic equation with interval coefficients References: In-Reply-To: Content-Type: multipart/mixed; boundary="------------090408020206050502070202" X-DCC-ZID-Univie-Metrics: mx7.univie.ac.at 4247; Body=5 Fuz1=5 Fuz2=5 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000018 This is a multi-part message in MIME format. --------------090408020206050502070202 Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit George Corliss wrote: > >>>It is described in the paper E. R. Hansen and G. W. Walster, Sharp bounds on >>>interval polynomial roots, Reliable Computing, 2002, Vol. 8, No. 2, pp. >>>115-122. >> >>Thanks. I hope they didn't patent it! > > They have applied for one. Patent application number: 20030055857 > Method and apparatus for computing roots of a polynomial equation with > interval coefficients > > You may view the application at > http://appft1.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&u=%2Fneta > html%2FPTO%2Fsearch-adv.html&r=16&p=1&f=G&l=50&d=PG01&S1=walster.IN.&OS=IN/w > alster&RS=IN/walster Ultimately their patents will just mean that, for fear of possible law suits, nobody apart from SUN will be using the results of their research, but instead use innocent replacements. Using the latter may even be an advantage, as in the present case. The algorithm they try to patent sometimes gives a gross overestimation of the zero set. For example, in BACKGROUND [0018],[0019],[0064],[0065], one gets [-inf,inf] if A=B=0 notin C, although the solution set is empty. It seems that it is implicitly assumed that A is nonzero. Their formulas also lead to overflow when B.sup^2 > realmax, with very poor results if A=C=B/2 and B is huge. In order to prevent that there will be a patent on similar elementary tasks, I post a solution for the constraint propagation on univariate quadratic expressions, with or without interval coefficents. dvi,ps,and pdf versions can be downloaded from the address given below; the latex original is attached here to document that the paper was created today. Arnold Neumaier ======================================================================= A. Neumaier Constraint propagation for univariate quadratic constraints Manuscript (January 5, 2005) http://www.mat.univie.ac.at/~neum/papers.html#cpquad Abstract We present formulas for rigorous constraint propagation of quadratic equality or inequality constraints involving a single nonlinear variable. Since the analysis is very elementary, probably everything in here was known for a long time. The present approach, based on directed rounding only, provide efficient alternatives to the procedures discussed by E. R. Hansen and G. W. Walster, Sharp bounds on interval polynomial roots, Reliable Computing 8 (2002), 115--122. (who only treat the solution of a quadratic equation with interval coefficients, and treat incorrectly the case where the coefficient of the quadratic term contains numbers of both signs), which employ interval arithmetic. In view of pending patent applications by these authors, who by these activities threaten to curb the freedom of research on interval methods, the following is explicitly stated: Various modifications to the methods described will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to such modifications without departing from the spirit and scope of the present methods. Thus, the present methods are not intended to be limited to the formulas shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein. --------------090408020206050502070202 Content-Type: application/x-tex; name="cpquad.tex" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="cpquad.tex" \documentclass[12pt]{article} \def\a {{\bf a}} \def\b {{\bf b}} \def\c {{\bf c}} \def\x {{\bf x}} \def\ol{\overline} \def\ul{\underline} \parindent0pt \parskip 2ex plus 1pt minus 1pt \begin{document} \begin{center} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% {\LARGE \bf Constraint propagation for } \\ {\LARGE \bf univariate quadratic constraints} \\ \vspace{1cm} \centerline{\sl {\large \bf Arnold Neumaier}} \vspace{0.5cm} \centerline{\sl Institut f\"ur Mathematik, Universit\"at Wien} \centerline{\sl Strudlhofgasse 4, A-1090 Wien, Austria} \centerline{\sl email: Arnold.Neumaier [at] univie [dot] ac.at} \centerline{\sl WWW: http://www.mat.univie.ac.at/$\sim$neum/} \end{center} \vspace{0.5cm} \hfill January 5, 2004 \vspace{0.5cm} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% {\bf Abstract.} We present formulas for rigorous constraint propagation of quadratic equality or inequality constraints involving a single nonlinear variable. Since the analysis is very elementary, probably everything in here has been known for a long time. The present approach, based on directed rounding only, provides efficient alternatives to the procedures discussed by {\sc Hansen \& Walster} \cite{HanW} (who only treat the solution of a quadratic equation with interval coefficients, and treat incorrectly the case where the coefficient of the quadratic term contains numbers of both signs), which employ interval arithmetic. In view of pending patent applications by these authors, who by these activities threaten to curb the freedom of research on interval methods, the following is explicitly stated: Various modifications to the methods described will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to such modifications without departing from the spirit and scope of the present methods. Thus, the present methods are not intended to be limited to the formulas shown, but are to be accorded the widest scope consistent with the principles and features disclosed herein. Notation is as in my book {\sc Neumaier} \cite{Neu.int}. \newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Bounds for quadratic expressions} To find a rigorous upper bound on \[ u=\sup\,\{ax^2+bx \mid x \in \x\}, \] we note that \[ u=\max\,\{\ul x(a\ul x+b),\ol x(a\ol x+b)\}, \] except in case that $ax^2+bx$ attains its global maximum in the interior of $\x$. This is the case iff $a<0$ and $t=-b/(2a)$ is in the interior of $\x$, in which case $u=b^2/(-4a)$, attained at $t$. If $\ul x\ge0$, we get a rigorous upper bound in finite precision arithmetic by computing with upward rounding as follows ({\tt xl} = $\ul x$, {\tt xu} = $\ol x$): \begin{verbatim} roundup; u=max(xl*(a*xl+b),xu*(a*xu+b)); s=b/2; t=s/(-a); if t>xl, r=(-2*a)*xu; if r>b, u=max(u,s*t); end; end; \end{verbatim} With some extra analysis, it could be determined in most cases which of the three cases is the worst case; however, if the unconstrained maximum of the quadratic is very close to a bound (or to both bounds), two (or three) of the cases might apply due to uncertainty caused by rounding errors. \bigskip Finding a rigorous enclosure for the interval \[ \c=\sup\,\{ax^2+bx \mid x \in \x,~ a \in \a,~ b\in \b\} \] can be reduced to the above for $\ul x \ge 0$, using \[ \ol c = \sup\, \{\ol ax^2+\ol bx \mid x \in \x\},~~~ \ul c = -\sup\, \{-\ul ax^2-\ul bx \mid x \in \x\}. \] The case $\ol x\le0$ can be reduced to this by changing the sign of $x$, and the general case by splitting $\x$ at zero if necessary. \bigskip Essentially the same analysis holds for rigorous upper bounds on \[ u=\sup\Big\{~\sum_{i=1}^{n} a_i x^i ~\Big|~ x \in \x~\Big\} \] and for rigorous enclosures of \[ \c=\sup\Big\{~\sum_{i=1}^{n} a_i x^i ~\Big|~ x \in \x,~ a\in\a~\Big\}, \] except that finding the interior extrema is more involved. It can be done with closed formulas for $n\le 5$ (though already $n=4$ is quite cumbersome and not recommended), and in general (recommended for $n>3$) using a root enclosure algorithm for the derivative, such as that in {\sc Neumaier} \cite{Neu.roots}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Solving quadratic constraints} To find the set \[ X=\{x \ge 0 \mid ax^2+2bx \ge c\}, \] we proceed as follows. If $a=0$, the constraint is in fact linear, and we have \[ X= \cases{ \emptyset & if $c>0$, $b\le 0$,\cr [0.5c/b,\infty] & if $c>0$, $b>0$, \cr [0,0.5c/b] & if $c\le 0$, $b<0$, \cr [0,\infty] & if $c\le 0$, $b\ge 0$, } \] which can be nested such that only two compares are needed in any particular case. For a rigorous enclosure in finite precision arithmetic, rounding must be downwards in the second case, and upwards in the third case. If $a \ne 0$, the behavior is governed by the zeros of the quadratic equation $ax^2+2bx-c=0$, given by \[ t_1=\frac{-b-\sqrt{\Delta}}{a}=\frac{c}{b-\sqrt{\Delta}},~~~~~~~~~ t_2=\frac{-b+\sqrt{\Delta}}{a}=\frac{c}{b+\sqrt{\Delta}}, \] where $\Delta:=b^2+ac$. If $\Delta\ge 0$, the zeros are real and the nonnegative zeros determine \[ X=\cases{ [0,\infty]\setminus~]t_1,t_2[ & if $a>0$,\cr [0,\infty]\cap\, [t_2,t_1] & if $a<0$. } \] Depending on the signs of $a$, $b$ and $c$ we find \[ X=\cases{ \emptyset & if $a< 0$, $b\le 0$, $c> 0$,\cr [0,-(c/z)] & if $a< 0$, $b\le 0$, $c\le 0$,\cr [0,z/(-a)] & if $a< 0$, $b\ge 0$, $c\le 0$,\cr [-((-c)/z),z/(-a)] & if $a< 0$, $b\ge 0$, $c> 0$,\cr [0,-(c/z)]\cup[z/a,\infty] & if $a> 0$, $b\le 0$, $c\le 0$,\cr [z/a,\infty] & if $a> 0$, $b\le 0$, $c> 0$,\cr [-((-c)/z),\infty] & if $a> 0$, $b\ge 0$, $c> 0$,\cr [0,\infty] & if $a> 0$, $b\ge 0$, $c\le 0$, } \] where \[ z=|b|+\sqrt{\Delta}. \] These formulas are numerically stable, and can be nested such that only three compares are needed in any particular case. (There are avoidable overflow problems for huge $|b|$, which can be cured by using for huge $|b|$ instead of $\sqrt{b^2+ac}$ the formula $|b|\sqrt{1+ac/b^2}$.) Rigorous results in the presence of rounding errors are obtained if lower bounds are rounded downwards, and upper bounds are rounded upwards. With the bracketing as given, this happens if in cases 2,5 and 6 all computations (including those of $\Delta=\sqrt{b^2+ac}$ and $z=|b|+\sqrt{\Delta}$) are done with rounding downwards, and in the other cases with rounding upwards. (However, this does {\bf not} hold for the version guarded against overflow, where further care is needed for the directed rounding of $\sqrt{\Delta}=|b|\sqrt{1+ac/b^2}$.) If (the exact) $\Delta$ is negative, there is no real solution, and $X$ is empty if $c>0$ and $[0,\infty]$ otherwise. The case when the sign of $\Delta$ cannot be determined due to rounding errors needs special consideration. In the first and last case, the conclusion holds independent of the sign of $\Delta$, so that the latter need only be computed for cases 2--7. In the cases 2, 3, 6, and 7 we have $ac\ge 0$, so that $\Delta\ge 0$ automatically. This leaves cases 4 and 5. Now it is easily checked that with the recommended rounding and, in place of cases 4 and 5, \[ X=\cases{ \emptyset & if $a< 0$, $b\ge 0$, $c> 0$, $\Delta< 0$,\cr [-((-c)/z),z/(-a)] & if $a< 0$, $b\ge 0$, $c> 0$, $\Delta\ge 0$,\cr [0,-(c/z)]\cup[z/a,\infty] & if $a> 0$, $b\le 0$, $c\le 0$, $\Delta\ge 0$,\cr [0,\infty] & if $a> 0$, $b\le 0$, $c\le 0$, $\Delta< 0$, } \] a rigorous enclosure is computed in all cases. \bigskip Finding the set \[ X'=\{x \ge 0 \mid ax^2+2bx \in \c \mbox{ for some } a\in\a, b\in\b\} \] can be reduced to the previous task since \[ X'=\{x \ge 0 \mid \ul a x^2+2\ul b x \le \ol c\} \cap \{x \ge 0 \mid \ul a x^2+2\ul b x \le \ol c\}. \] The sets \[ X''=\{x \in \x_0 \mid ax^2+2bx \ge c\} \] and \[ X'''=\{x\in\x_0 \mid ax^2+2bx \in\c \mbox{ for some } a\in\a, b\in\b\} \] can be obtained by intersecting the result of the above tasks with $\x_0$ if $\ul x_0\ge0$, by negating $x$, $\x_0$, and $\b$ if $\ol x_0\le 0$, and by splitting $\x_0$ at zero if $0$ is in the interior of $\x_0$. By modifying the code appropriately, one can also avoid computing roots which can be seen to lie outside $\x_0$. \bigskip With minor changes, these formulas also apply for strict inequalities and interior enclosures. Also, it is clear that polynomial inequalities and inclusions of interval polynomials can be solved by a straightforward adaptation of the above arguments. \bigskip %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{thebibliography}{99} \bibitem{HanW} E. R. Hansen and G. W. Walster, Sharp bounds on interval polynomial roots, Reliable Computing 8 (2002), 115--122. \bibitem{Neu.int} A. Neumaier, Interval Methods for Systems of Equations, Cambridge Univ. Press, Cambridge 1990. \bibitem{Neu.roots} A. Neumaier, Enclosing clusters of zeros of polynomials, J. Comput. Appl. Math. 156 (2003), 389--401. \end{thebibliography} \end {document} --------------090408020206050502070202-- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 5 06:03:45 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j05C3inu001665 for ; Wed, 5 Jan 2005 06:03:44 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j05C3i6t001664 for reliable_computing-outgoing; Wed, 5 Jan 2005 06:03:44 -0600 (CST) Received: from imap.univie.ac.at (mailbox-lmtp.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j05C3YJY001659 for ; Wed, 5 Jan 2005 06:03:40 -0600 (CST) Received: from univie.ac.at (theseus.mat.univie.ac.at [131.130.16.23]) by imap.univie.ac.at (8.12.10/8.12.10) with ESMTP id j05C3I0W235852; Wed, 5 Jan 2005 13:03:20 +0100 Message-ID: <41DBD786.7000407 [at] univie [dot] ac.at> Date: Wed, 05 Jan 2005 13:03:18 +0100 From: Arnold Neumaier Organization: University of Vienna User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.4.3) Gecko/20041005 X-Accept-Language: en, de MIME-Version: 1.0 To: "r. corless" CC: George Corliss , Vladik Kreinovich , reliable_computing [at] interval [dot] louisiana.edu, rbk [at] louisiana [dot] edu Subject: Re: quadratic equation with interval coefficients References: In-Reply-To: Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-DCC-ZID-Univie-Metrics: mx9.univie.ac.at 4249; Body=6 Fuz1=6 Fuz2=6 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000019 r. corless wrote: > Interesting. I was speaking to an intellectual-property lawyer last week > (he will marry my sister-in-law in July, this is just family, I am not > applying for patents myself :-) and he pointed out to me that the > "hard" question for patents is not "originality" but "obviousness". A > patent will not be granted for something that is "obvious" to someone > "skilled in the art". > > I understand that phrase "skilled in the art" to mean an ordinarily > competent interval practitioner in this case, and not to someone elite > (and it is clear that there are elite practitioners on this mailing list, > to be sure). > > So, here's the question for the community: Is the solution of > interval polynomials "obvious", given competent knowledge of interval > arithmetic? > > Would you set it on an exam? The only case worked out in detail by Hansen and Walster is that of quadratics. With some simple hints, a complete solution for quadratics can be found by diligent students in a few hours, at the same level of quality as Hansen and Walster's, or even better. Indeed, they write on p.119 of their paper, ''The simpler algorithm has probably also been often used; but the authors are unaware of any publication describing it.'' Thus they admit that the contents is ''readily apparent to practitioners skilled in the art'' (a quote from their patent application; they use it in an opposite context), and hence not patentable. What do the law experts say? Everything is in fact very elementary. The only difficulty is that there are many cases to consider, more than an average student would have the guts to consider. So the students should be told that they need to use monotonicity arguments and have to consider 16 cases, depending on the signs of a,b,c,x. See my other mail for a neatly polished solution, with all bells and whistles (which probably could be expected only by very good students). It takes much less work than the procedure of Hansen and Walster who always compute up to 8 interval enclosures of roots. Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 5 06:28:17 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j05CSHeL001808 for ; Wed, 5 Jan 2005 06:28:17 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j05CSHOr001807 for reliable_computing-outgoing; Wed, 5 Jan 2005 06:28:17 -0600 (CST) Received: from imap.univie.ac.at (mailbox-lmtp.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j05CS7EA001803 for ; Wed, 5 Jan 2005 06:28:13 -0600 (CST) Received: from univie.ac.at (theseus.mat.univie.ac.at [131.130.16.23]) by imap.univie.ac.at (8.12.10/8.12.10) with ESMTP id j05CRu0W416148; Wed, 5 Jan 2005 13:27:58 +0100 Message-ID: <41DBDD4C.2010009 [at] univie [dot] ac.at> Date: Wed, 05 Jan 2005 13:27:56 +0100 From: Arnold Neumaier Organization: University of Vienna User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.4.3) Gecko/20041005 X-Accept-Language: en, de MIME-Version: 1.0 To: Arnold Neumaier CC: George Corliss , Vladik Kreinovich , reliable_computing [at] interval [dot] louisiana.edu, rbk [at] louisiana [dot] edu Subject: Re: quadratic equation with interval coefficients References: <41DBD4C9.70406 [at] univie [dot] ac.at> In-Reply-To: <41DBD4C9.70406 [at] univie [dot] ac.at> Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-DCC-ZID-Univie-Metrics: mx9.univie.ac.at 4249; Body=5 Fuz1=5 Fuz2=5 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000020 Arnold Neumaier wrote: > The present approach, based on directed rounding only, provide > efficient alternatives to the procedures discussed by > E. R. Hansen and G. W. Walster, > Sharp bounds on interval polynomial roots, > Reliable Computing 8 (2002), 115--122. > (who only treat the solution of a quadratic equation with interval > coefficients, and treat incorrectly the case where the coefficient > of the quadratic term contains numbers of both signs), > which employ interval arithmetic. Actually their treatment is correct and my understanding of their algorithm was at first mistaken; I had forgotten to take this comment out of the abstract. Sorry. Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 5 17:20:17 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j05NKGYl002922 for ; Wed, 5 Jan 2005 17:20:16 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j05NKGPo002921 for reliable_computing-outgoing; Wed, 5 Jan 2005 17:20:16 -0600 (CST) Received: from mail.gmx.net (pop.gmx.net [213.165.64.20]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with SMTP id j05NK6GF002917 for ; Wed, 5 Jan 2005 17:20:13 -0600 (CST) Received: (qmail invoked by alias); 05 Jan 2005 23:19:57 -0000 Received: from dialin-145-254-197-199.arcor-ip.net (EHLO gmx.net) (145.254.197.199) by mail.gmx.net (mp009) with SMTP; 06 Jan 2005 00:19:57 +0100 X-Authenticated: #5874409 Message-ID: <41DC7608.5000806 [at] gmx [dot] net> Date: Thu, 06 Jan 2005 00:19:36 +0100 From: Jens Maurer User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.4) Gecko/20030624 Netscape/7.1 X-Accept-Language: en-us, en MIME-Version: 1.0 To: interval CC: "Nelson H. F. Beebe" , Arnold Neumaier Subject: Re: Costs of floating-point rounding control and predecessor/successor computation References: In-Reply-To: Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-Y-GMX-Trusted: 0 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000021 Nelson H. F. Beebe wrote: > While I cannot comment on the efficiency of Matlab's rounding mode > access in the Intlab package, I can supply fresh evidence that it > should have minimal cost. > > On IA-32, rounding mode access is available via the floating-point > control word, which takes only one instruction to fetch or set. While I can't comment on the efficiency of rounding mode access in interpreted languages, I would like to point out that rounding mode changes usually cause a complete pipeline flush in modern processors, i.e. the processor waits until all previous operations have completed. On a Pentium 4, this is much more visible than on a Pentium III due to much longer pipelines on the P4. The code for (k = 1; k <= 100000000; ++k) sum += BASE; takes 0.96 sec on my Pentium III 850 Mhz, compared to 2.3 sec for 1/100 the work in Nelson Beebe's interpreted language on his 600 MHz CPU. (The overhead of the interpreted language is a factor of 200 in this particular case.) Adding another addition (here: subtraction) for (k = 1; k <= 100000000; ++k) { sum += BASE; sum -= 0.5; } now takes 1.32 sec on my machine, clearly showing the pipeline effects: We're doing twice the number of floating-point operations, but we need a meagre 30% additional time. Adding a setting of the rounding mode instead of the second addition, the loop now takes 2.87 sec on my machine, thus the differences are much larger than those visible in the interpreted language. My C library's nextafter() function is about 10 times slower on subnormals than on normals (using glibc 2.3.3). Jens Maurer From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Jan 6 09:40:29 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j06FeTp8000756 for ; Thu, 6 Jan 2005 09:40:29 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j06FeS9a000755 for reliable_computing-outgoing; Thu, 6 Jan 2005 09:40:28 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j06FeKsK000751 for ; Thu, 6 Jan 2005 09:40:26 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j06FeD601404 for ; Thu, 6 Jan 2005 08:40:15 -0700 (MST) Message-Id: <200501061540.j06FeD601404 [at] cs [dot] utep.edu> Date: Thu, 6 Jan 2005 08:40:13 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: ECC-CDC2005 invited session on INTERVAL COMPUTATIONS To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=ISO-8859-1 Content-MD5: KzQ8LpqDU720MiwDM34wcQ== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from QUOTED-PRINTABLE to 8bit by interval.louisiana.edu id j06FeQsK000752 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000022 forwarding; apologies for multiple copies ------------- Begin Forwarded Message ------------- From: Nacim RAMDANI Dear colleagues This mail is an invitation to participate to an invited session I plan to organize during the ECC-CDC 2005 conference http://www.esi2.us.es/~cdcecc05/, dealing with theory and application of interval computations. Interval analysis has been used since more than a decade now, in both applied mathematics and engineering. On the one hand, it is a reliable tool for uncertainty propagation and thus is used for computing rigorous error bounds when evaluating functions or solving differential equations. On the other hand, allied with constraint propagation, interval analysis becomes a powerful tool for solving, in a guaranteed way, engineering problems such as global optimization, bounded-error estimation or robust control. The invited session aims at bringing together researchers from the interval computations community in order to carry out presentations and discussions of recent advances in the field. If you are interested to participate to this invited session, and I hope you will, please let me know as soon as possible. Please also note that the deadline for submission is March 1st, therefore if you intend to participate to this session, please send the full paper in the correct format, to ramdani@univ-paris12.fr, no later than february 28th. Looking forward reading from you soon. Best Regards Dr Nacim RAMDANI I wish you a happy new year 2005. Je vous présente mes meilleurs voeux pour la nouvelle année 2005. Nacim RAMDANI Maître de Conférences phone : +33 (0)1 45 17 18 36 mobile : +33 (0)6 17 83 35 42 email : ramdani@univ-paris12.fr CERTES - UPRES-EA 3481 IUT de Créteil - Université PARIS XII http://www.univ-paris12.fr Ave du Général de Gaulle F-94010 CRETEIL CEDEX phone : +33 (0)1 45 17 18 50 fax : +33 (0)1 45 17 65 51 site web du GT Identification http://gtident.cran.uhp-nancy.fr/ site web du GT Méthodes Ensemblistes http://www-lag.ensieg.inpg.fr/gt-ensembliste/ ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Jan 6 22:00:28 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0740SOq001692 for ; Thu, 6 Jan 2005 22:00:28 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0740RrW001691 for reliable_computing-outgoing; Thu, 6 Jan 2005 22:00:27 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0740J8O001686 for ; Thu, 6 Jan 2005 22:00:25 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j0740Dn05594; Thu, 6 Jan 2005 21:00:13 -0700 (MST) Message-Id: <200501070400.j0740Dn05594 [at] cs [dot] utep.edu> Date: Thu, 6 Jan 2005 21:00:14 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Extended deadlines for Virtual Concept 2005 To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu Cc: martineceberio [at] yahoo [dot] com MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: zoFDEGx0t6k5nn4+cojtRA== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000023 forwarding ------------- Begin Forwarded Message ------------- To: martineceberio [at] yahoo [dot] com From: VIRTUALCONCEPT_PUBLICITY/LIPSI/ESTIA/CCIBPB [at] bayonne [dot] cci.fr Dear Colleague, due to Christmas time, a lot of authors wanting to submit an abstract to Virtual Concept 2005 have asked us a possibility for extending deadlines. Deadlines for abstract submissions have been extended to the 4th of February. Other dates are still the same. You can submit a 200 words abstract on our website for: - an article: http://www.virtualconcept.estia.fr/call4paper.php?logout=1 - an invited session: http://www.virtualconcept.estia.fr/call4invited.php?logout=1 - a tutorial: http://www.virtualconcept.estia.fr/call4tutorial.php?logout=1 It will be an honor for us to welcome you in Virtual Concept 2005 that will foresee to gather more than 500 people interested by the use of Virtual Reality and Simulation in Industry. Happy Christmas and happy new year. Publicity and Scientific Committee Chairs of Virtual Concept 2005 ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Jan 7 05:52:46 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j07BqjU6002686 for ; Fri, 7 Jan 2005 05:52:45 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j07Bqj5T002685 for reliable_computing-outgoing; Fri, 7 Jan 2005 05:52:45 -0600 (CST) Received: from shiva.bio.bas.bg (bas-bio.lines.bas.bg [195.96.252.58]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j07BqNuF002681 for ; Fri, 7 Jan 2005 05:52:42 -0600 (CST) Received: from biomath8 (ihost_0_172.bio.bas.bg [10.0.0.172]) by shiva.bio.bas.bg (8.12.10/8.12.10) with ESMTP id j07BqE8k002064 (version=TLSv1/SSLv3 cipher=DES-CBC3-SHA bits=168 verify=NO); Fri, 7 Jan 2005 13:52:14 +0200 From: "Svetoslav Markov" To: Arnold Neumaier Date: Fri, 07 Jan 2005 13:52:13 +0200 MIME-Version: 1.0 Subject: Re: quadratic equation with interval coefficients CC: Message-ID: <41DE940D.11260.FD069F@localhost> In-reply-to: <41D9984B.3070901 [at] univie [dot] ac.at> X-mailer: Pegasus Mail for Windows (4.21c) Content-type: text/plain; charset=US-ASCII Content-transfer-encoding: 7BIT Content-description: Mail message body Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000024 Dear Arnold, the solution of a single quadratic equation in one variable with interval coefficients has been discussed in detail in Section 4 of the paper: N. S. Dimitrova, S. M. Markov. Ueber die intervall-arithmetische Berechnung des Wertebereichs einer Funktion mit Anwendungen, Freiburger Intervall-Berichte, Univ. Freiburg, 81/4 (1981), 1--22. Svetoslav Markov On 3 Jan 2005 at 20:08, Arnold Neumaier wrote: > Is there a complete discussion in the literature of the solution > of a single quadratic equation in one variable, > with interval coefficients? Perhaps even an implementation > that computes a correctly rounded enclosure for the solution set? > > I worked out a solution myself, but this problem is so natural > that it was probably treated before. > > > Arnold Neumaier > From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Jan 7 09:39:21 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j07FdLTo003071 for ; Fri, 7 Jan 2005 09:39:21 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j07FdLqb003070 for reliable_computing-outgoing; Fri, 7 Jan 2005 09:39:21 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j07Fd45A003066 for ; Fri, 7 Jan 2005 09:39:18 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j07Fd1F08620; Fri, 7 Jan 2005 08:39:01 -0700 (MST) Message-Id: <200501071539.j07Fd1F08620 [at] cs [dot] utep.edu> Date: Fri, 7 Jan 2005 08:38:59 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: IFSA'05: deadline extended to January 17, 2005 To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: CsufoVDyYAerm4EQAU60Zg== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000025 We originally planned two interval-related sessions: Weldon Lodwick is planning to organize a session on fuzzy optimization and Chenyi Hu was planning to organize a session on intervals and fuzzy in general. It looks like we did not have anough people for the second session, so everyone interested in welcome to submit to Weldon Lodwick's session. Please note that the deadline for conference submissions has been extended to January 17, 2005. ------------- Begin Forwarded Message ------------- >>> "IFSA2005 Secretariat" ss). ... Thank you very much in advance! Best regards, IFSA2005/Beijing Secretariat School of Economics and Management Tsinghua University, Beijing 100084, China Phone/Fax: 86-10-62789925 Email: ifsa2005 [at] em [dot] tsinghua.edu.cn Webpage : http://ifsa2005.em.tsinghua.edu.cn/ >************************************************************************** >CALL FOR PAPERS >IFSA2005 World Congress >July 28-31, 2005, Beijing China >http://ifsa2005.em.tsinghua.edu.cn > >The 11th World Congress of International Fuzzy Systems Association >(IFSA 2005) will be held in Beijing China, July 28-31, 2005. As a >major bi-annual event of IFSA, the Congress aims at bringing together >scholars and practitioners from academia and industries to present the >latest development in theories and applications of fuzzy logic and >soft computing. The scientific program will include keynote/plenary >talks and technical parallel sessions that address important issues of >interest in the fields. The Congress will serve as a platform not only >for knowledge sharing, but also for stimulating new ideas in >broadening and deepening theoretical and applied explorations of fuzzy >logic and soft computing. Notably, IFSA2005 will take place in the >year of IFSA's 20th anniversary, which may well be an event of memory >and celebration in the course of its evolution. > >This IFSA World Congress is to be the first-time-ever in Mainland >China. China is a dynamic nation with a rapid economic growth and huge >market. The conference site is Beijing, which has been the capital of >China for about five hundred years, and is now one of the largest >international cities in the world. Nowadays, as the cultural, >educational and Hi-tech center of the nation, Beijing possesses a >large number of world-class conference facilities, communication >infrastructures and hotels, and has successfully hosted many important >international conferences. In addition, Beijing is an ideal place for >sightseeing. Its rich cultures and historical attractions such as the >Great Wall, Forbidden City, Summer Palace, and Temple of Heaven will >provide participants with unique experiences for social activities. > >Topics >We solicit papers on theoretical issues and their applications related >to fuzzy logic and soft computing. Suggested topics include but are >not limited to: >* Mathematical Foundations of Fuzzy Set Theory >* Fuzzy Logic and Approximate Reasoning >* Neural Networks, Genetic Algorithms and Soft Computing >* Fuzzy Control, Robots and Intelligent Techniques >* Expert Systems and Computational Intelligence >* Knowledge Discovery and Data Mining >* Rough Sets and Evidence Theory >* Uncertainty in Decision Sciences and Optimization >* Signal/Image Processing and Pattern Recognition >* Fuzzy Databases and Information Retrieval >* Hybrid Systems > >Honorary Chair: Lotfi A. Zadeh, USA >General Chair: Yingming Liu, China >Organizing Chair: Guoqing Chen, China >Program Chair: Mingsheng Ying, China > >Advisory Committee >Zeungnam Bien, Korea Witold Pedrycz, Canada >George J. Klir, USA Philippe Smets, Belgium >Laszlo T. Koczy, Hungary Michio Sugeno, Japan >Yingming Liu, China Lotfi A. Zadeh, USA >Ebrahim Mamdani, UK Chunjun Zhao, China >Zdzislaw Pawlak, Poland Hans-Jurgen Zimmermann, Germany > >Local Organization Committee > >Yixiang Chen, China >Dexue Zhang, China >Wenxiu Zhang, China >Chongyou Zheng, China > >Program Committee (Not Completed) > >M. Berthold (Germany) Maokang Luo (China) >James C. Bezdek (USA) Luis Magdalena (Spain) >Taner Bilgic (Turkey) Trevor Martin (UK) >Piero Bonissone (USA) Kyung Chan Min (Korea) >Bernadette Bouchon-Meunier (France) Masao Mukaidono (Japan) >Kai-Yuan Cai (China) Vesa Niskanen (Finland) >Christer Carlsson (Finland) Vilem Novak (Czech Republic) >Oscar Castillo (Mexico) Fred Petry (USA) >Guoqing Chen (China) Nguyen Hoang Phuong (Vietnam) >Didier Dubois (France) Henri Prade (France) >Takeshi Furuhashi (Japan) Arthur Ramer (Australia) >Giangiacomo Gerla (Italy) Frank Chung-Hoon Rhee (Korea) >Lluis Godo (Spain) Da Ruan (Belgium) >Fernando Gomide (Brazil) Elie Sanchez (France) >Kaoru Hirota (Japan) Sandra Sandri(Brazil) >Janusz Kacprzyk (Poland) Thomas Sudkamp (USA) >Okiay Kaynak (Turkey) I. Burhan Turksen (Canada) >Jim Keller (USA) M. Amparo Vila Miranda (Spain) >Etienne E. Kerre (Belgium) Guojun Wang (China) >Erich P. Klement (Austria) Li-Xin Wang (Hong Kong China) >Donald Kraft (USA) Paul P. Wang (USA) >Rudolf Kruse (Germany) Congxin Wu (China) >Jonathan Lee (Taiwan China) Ronald R. Yager (USA) >Hongxing Li (China) John Yen (USA) >C.T.Lin (Taiwan China) Mingsheng Ying (China) >Zhiqiang Liu (Hong Kong China) > >Important Dates > >Deadline for Submission: January 17, 2005 (extended) >Notification of Acceptance: February 28, 2005 >Final Version due: April 20, 2005 >Conference: July 28-31, 2005 > >Organized by >Fuzzy Mathematics and Fuzzy Systems Association of China > (The IFSA China Chapter) >Tsinghua University >Sichuan University >Supported by >National Natural Science Foundation of China >The Systems Engineering Society of China >China Automation Association >China Computer Federation >Chinese Mathematical Society > >Detailed information about the paper submission, proceedings, >registration, accommodation, journal special issues, student paper >award, conference program, etc., will be available at the conference >web site (http://ifsa2005.em.tsinghua.edu.cn) and in forthcoming >CFPs. You may also contact us at: > Professor Guoqing Chen > IFSA2005 Organizing Committee and Secretariat > School of Economics and Management > Tsinghua University, Beijing 100084, China > Tel./Fax: 86-10-62789925 > Email: ifsa2005 [at] em [dot] tsinghua.edu.cn > >------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Jan 10 10:56:31 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0AGuVKG009608 for ; Mon, 10 Jan 2005 10:56:31 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0AGuVtN009607 for reliable_computing-outgoing; Mon, 10 Jan 2005 10:56:31 -0600 (CST) Received: from imap.univie.ac.at (mailbox-lmtp.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0AGuLaL009603 for ; Mon, 10 Jan 2005 10:56:27 -0600 (CST) Received: from univie.ac.at (theseus.mat.univie.ac.at [131.130.16.23]) by imap.univie.ac.at (8.12.10/8.12.10) with ESMTP id j0AGtvMw355124; Mon, 10 Jan 2005 17:56:00 +0100 Message-ID: <41E2B39D.5000501 [at] univie [dot] ac.at> Date: Mon, 10 Jan 2005 17:55:57 +0100 From: Arnold Neumaier Organization: University of Vienna User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.4.3) Gecko/20041005 X-Accept-Language: en, de MIME-Version: 1.0 To: Svetoslav Markov CC: reliable_computing [at] interval [dot] louisiana.edu Subject: Re: quadratic equation with interval coefficients References: <41DE940D.11260.FD069F@localhost> In-Reply-To: <41DE940D.11260.FD069F@localhost> Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-DCC-ZID-Univie-Metrics: mx7.univie.ac.at 4247; Body=3 Fuz1=3 Fuz2=3 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000026 Svetoslav Markov wrote: > the solution of a single quadratic equation in one variable > with interval coefficients has been discussed in detail in > Section 4 of the paper: > > N. S. Dimitrova, S. M. Markov. Ueber die > intervall-arithmetische Berechnung des Wertebereichs einer Funktion > mit Anwendungen, Freiburger Intervall-Berichte, Univ. Freiburg, 81/4 > (1981), 1--22. A scanned copy of the paper (with thanks to Prof. Markov) is at http://www.mat.univie.ac.at/~neum/contrib/intquad.pdf Section 4 contains a complete discussion of the determination of { x | x^2 + p x + q = 0 for some p in \p, q in \q } for intervals \p, \q. This is slightly less general than what Hansen and Walster (and I) treat, where x^2 also has an interval coefficient. Note that simply dividing by this coefficient would result in overestimation of the solution set. Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 12 08:52:31 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0CEqUr9013566 for ; Wed, 12 Jan 2005 08:52:30 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0CEqUmp013565 for reliable_computing-outgoing; Wed, 12 Jan 2005 08:52:30 -0600 (CST) Received: from lakermmtao05.cox.net (lakermmtao05.cox.net [68.230.240.34]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0CEqBFp013561 for ; Wed, 12 Jan 2005 08:52:27 -0600 (CST) Received: from Inspiron-8200 ([68.226.133.93]) by lakermmtao05.cox.net (InterMail vM.6.01.04.00 201-2131-117-20041022) with SMTP id <20050112145205.JCYS16431.lakermmtao05.cox.net@Inspiron-8200> for ; Wed, 12 Jan 2005 09:52:05 -0500 Message-Id: <2.2.32.20050112145154.01131a6c [at] pop [dot] louisiana.edu> X-Sender: rbk5287 [at] pop [dot] louisiana.edu X-Mailer: Windows Eudora Pro Version 2.2 (32) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Wed, 12 Jan 2005 08:51:54 -0600 To: reliable_computing [at] interval [dot] louisiana.edu From: "R. Baker Kearfott" Subject: Freiburger Intervallberichte: Volunteer? Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000027 Colleagues, I see steady reference to articles in the "Freiburger Intervallberichte," and I personally have a need from time to time to look up articles therein. Also, my understanding is that, since Freiburger Intervallberichte was a preprint series, copyright issues are not involved. I see significant benefit in having electronic (i.e. scanned) copies of the Freiburger Intervallberichte on the web (such as on interval.louisiana.edu). However, someone will actually have to scan the series (ideally into PDF), a significant but not prohibitive task. We thus need a volunteer (or a volunteering of resources) to scan the series. Does anyone wish to volunteer? Also, does anyone have comments concerning this proposed endeavor? Sincerely, R. Baker Kearfott --------------------------------------------------------------- R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax) (337) 482-5270 (work) (337) 993-1827 (home) URL: http://interval.louisiana.edu/kearfott.html Department of Mathematics, University of Louisiana at Lafayette (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) Box 4-1010, Lafayette, LA 70504-1010, USA --------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 12 08:59:46 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0CExkJX013681 for ; Wed, 12 Jan 2005 08:59:46 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0CExkMj013680 for reliable_computing-outgoing; Wed, 12 Jan 2005 08:59:46 -0600 (CST) Received: from baobab.unisa.it (baobab.unisa.it [193.205.160.136]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0CExZ7I013676 for ; Wed, 12 Jan 2005 08:59:41 -0600 (CST) Received: from plportatile (niki.diiie.unisa.it [193.205.164.127]) by baobab.unisa.it (8.13.2/8.13.2) with SMTP id j0CEx8vX514115 for ; Wed, 12 Jan 2005 15:59:18 +0100 (CET) Message-ID: <00b401c4f8b7$4de76350$7fa4cdc1@plportatile> From: "Patrizia Lamberti" To: Subject: polynomial variability Date: Wed, 12 Jan 2005 15:59:09 +0100 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_00AE_01C4F8BF.A6A0E220" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Spam-Score: (-4.687) BAYES_00,HTML_60_70,HTML_MESSAGE X-Scanned-By: MIMEDefang 2.42 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000028 This is a multi-part message in MIME format. ------=_NextPart_000_00AE_01C4F8BF.A6A0E220 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable I am a PhD Student in Information and Electric Engineering at the = University of Salerno, Italy. =20 I am investigating the possibility of determining the range of minimum = variability of a polynomial by means of interval analysis. =20 I prefer to describe the problem by using a simple example. =20 Let us consider the 5th order polynomial = f(x)=3Dx^5+60*x^4+30*x^3-10*x^2+6, which has 2 minima and 3 maxima in = the range I=3D[-1.0,0.7]. Let us inspect the behaviour of f over I by = considering a translating WIDE interval = X(k)=3D[x0(k)-delta,x0(k)+delta], included in I, with = x0=3D{-0.7,-0.6,.,0.3,0.4} and delta=3D0.3. Let us calculate the Taylor = expansion of f(x) centred in x0(k), k=3D1,2,., and evaluate its interval = extension F_TM(X(k)). I have found that, among the N values F_TM(X(k)) calculated, the one of = minimum radius is obtained for the X(k) wherein the real function f(x) = is subjected to the minimum variation (namely, in that X(k) the united = extension of f(X(k)) assumes the minimum radius). =20 Note that: 1) the F_TM(X(k)) are calculated over intervals X(k) of fixed, and = big, amplitude 2*delta; 2) I don't have looked for the true range of f over I or X(k), but = I it was enough for me to look for the range of minimum (even if = unknown) radius of f(x). =20 Now, I have some questions: 1) is this result of general validity, namely for any polynomial = and/or function in general? Does it exist some theorem helpful to = demonstrate it in general? 2) has this problem already afforded in literature? =20 Please, do not hesitate to ask for further details. =20 Best regards =20 Patrizia Lamberti =20 ------=_NextPart_000_00AE_01C4F8BF.A6A0E220 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

I am a PhD Student in Information and = Electric=20 Engineering at the University of = Salerno,=20 Italy.

 

I am investigating the possibility of = determining the=20 range of minimum variability of a polynomial by means of interval=20 analysis.

 

I prefer to describe the problem by using a = simple=20 example.

 

Let us consider the 5th = order=20 polynomial f(x)=3Dx^5+60*x^4+30*x^3-10*x^2+6, which has 2 minima and 3 = maxima in=20 the range I=3D[-1.0,0.7]. Let us inspect the behaviour of f over I by = considering=20 a translating WIDE interval X(k)=3D[x0(k)-delta,x0(k)+delta], included = in I, with=20 x0=3D{-0.7,-0.6,=85,0.3,0.4} and delta=3D0.3. Let us calculate the=20 Taylor expansion of f(x) = centred in x0(k),=20 k=3D1,2,=85, and evaluate its interval extension=20 F_TM(X(k)).

I have found that, among the N values = F_TM(X(k))=20 calculated, the one of minimum radius is obtained for the X(k) wherein = the real=20 function f(x) is subjected to the minimum variation (namely, in that = X(k) the=20 united extension of f(X(k)) assumes the minimum=20 radius).

 

Note that:

1)     =20 the F_TM(X(k)) are calculated over intervals X(k) of fixed, and = big,=20 amplitude 2*delta;

2)     =20 I don=92t have looked for the true range of f over I or X(k), = but I it was=20 enough for me to look for the range of minimum (even if unknown) radius = of=20 f(x).

 

Now, I have some=20 questions:

1)     =20 is this result of general validity, namely for any polynomial = and/or=20 function in general? Does it exist some theorem helpful to demonstrate = it in=20 general?

2)     =20 has this problem already afforded in=20 literature?

 

Please, do not hesitate to ask for further=20 details.

 

Best = regards

 

Patrizia = Lamberti

 

<= /HTML> ------=_NextPart_000_00AE_01C4F8BF.A6A0E220-- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 12 16:46:45 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0CMkiMb014378 for ; Wed, 12 Jan 2005 16:46:44 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0CMkioK014377 for reliable_computing-outgoing; Wed, 12 Jan 2005 16:46:44 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0CMkgnr014373 for ; Wed, 12 Jan 2005 16:46:42 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0CMkfG3014372 for reliable_computing [at] interval [dot] louisiana.edu; Wed, 12 Jan 2005 16:46:41 -0600 (CST) Received: from mail.math.berkeley.edu (mail.math.Berkeley.EDU [169.229.58.57]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0CLREtR014241 for ; Wed, 12 Jan 2005 15:27:24 -0600 (CST) Received: from megan (adsl-67-123-166-211.dsl.sntc01.pacbell.net [67.123.166.211]) (authenticated bits=0) by mail.math.berkeley.edu (8.13.2/8.12.11) with ESMTP id j0CLR1ZH072155 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NO); Wed, 12 Jan 2005 13:27:02 -0800 (PST) (envelope-from njw [at] math [dot] berkeley.edu) Message-ID: <001c01c4f8ed$75f45160$6500a8c0@megan> From: "Jiawang Nie" To: "Patrizia Lamberti" , Cc: "James Demmel" References: <00b401c4f8b7$4de76350$7fa4cdc1@plportatile> Subject: Re: polynomial variability Date: Wed, 12 Jan 2005 13:27:02 -0800 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0019_01C4F8AA.66FEA630" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Scanned-By: MIMEDefang 2.49 on 169.229.58.57 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000029 This is a multi-part message in MIME format. ------=_NextPart_000_0019_01C4F8AA.66FEA630 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Dear Patrizia: Your question about polynomial variability is very interesting, and r= elated to our work.=20 The global minimum or maximum of a univariate polynomial on an interv= al [a,b] can be found very efficiently by software SOSTOOLS or Gloptipoly (= search in google for the references and websits). So the true range of f(x= ) over your X(k) can be found.=20 The interval extensions F_TM(X(k)) evaluated via taylor expansion ( f= irst order ?) of f(x) reflect the true range of f(x) over X(k) when delta = is tiny. If delta is not sufficiently small, the relationship may not be cl= ear. =20=20=20=20=20=20=20=20 A more general problem about sensitivity analysis of solutions to p= olynomial systems is discussed in one of our papers. The following paper m= ay be useful to you: http://front.math.ucdavis.edu/math.OC/0411122 Given a multivariate system of polynomials p(x,mu), where the mu's can be = thought of as parameters determining the coefficient of p(), we give an alg= orithm for computing the minimal ellipsoid contining all the real solution= s x of p(x,mu)=3D0. For example, if q() is a single polynomial in the scal= ar x with coefficients in=20 intervals with given centers and radii, and you want bounds on the real zer= os,then this can be formulated as finding the minimum ellipsoid containing= the roots x of a system like sum_{i=3D0 to n} mu_i * x^i =3D 0 (mu_i - center_i)^2 + mu'_i^2 =3D radius^2 for i =3D 0 to n The paper uses techniques from semidefinite programming. Regards, Jiawang Nie and Jim Demmel ----- Original Message -----=20 From: Patrizia Lamberti=20 To: reliable_computing [at] interval [dot] louisiana.edu=20 Sent: Wednesday, January 12, 2005 6:59 AM Subject: polynomial variability I am a PhD Student in Information and Electric Engineering at the Univers= ity of Salerno, Italy. =20=20=20 I am investigating the possibility of determining the range of minimum va= riability of a polynomial by means of interval analysis. =20=20=20 I prefer to describe the problem by using a simple example. =20=20=20 Let us consider the 5th order polynomial f(x)=3Dx^5+60*x^4+30*x^3-10*x^2+= 6, which has 2 minima and 3 maxima in the range I=3D[-1.0,0.7]. Let us insp= ect the behaviour of f over I by considering a translating WIDE interval X(= k)=3D[x0(k)-delta,x0(k)+delta], included in I, with x0=3D{-0.7,-0.6,.,0.3,0= .4} and delta=3D0.3. Let us calculate the Taylor expansion of f(x) centred = in x0(k), k=3D1,2,., and evaluate its interval extension F_TM(X(k)). I have found that, among the N values F_TM(X(k)) calculated, the one of m= inimum radius is obtained for the X(k) wherein the real function f(x) is su= bjected to the minimum variation (namely, in that X(k) the united extension= of f(X(k)) assumes the minimum radius). =20=20=20 Note that: 1) the F_TM(X(k)) are calculated over intervals X(k) of fixed, and b= ig, amplitude 2*delta; 2) I don't have looked for the true range of f over I or X(k), but I= it was enough for me to look for the range of minimum (even if unknown) ra= dius of f(x). =20=20=20 Now, I have some questions: 1) is this result of general validity, namely for any polynomial and= /or function in general? Does it exist some theorem helpful to demonstrate = it in general? 2) has this problem already afforded in literature? =20=20=20 Please, do not hesitate to ask for further details. =20=20=20 Best regards =20=20=20 Patrizia Lamberti =20=20=20 ------=_NextPart_000_0019_01C4F8AA.66FEA630 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Content-Disposition: inline   Dear  Patrizia:         Yo= ur question about=20 polynomial variability is very interesting, and related to our work.=20         Th= e global minimum=20 or maximum of a univariate polynomial on an interval [a,b] can be found ver= y=20 efficiently by software SOSTOOLS or Gloptipoly ( search in google for the= =20 references and websits). So the true range of f(x)  over your X(k) can= be=20 found.         Th= e interval=20 extensions F_TM(X(k)) evaluated via= taylor=20 expansion ( first order ?) of  f(x) reflect the true range of f(x) ove= r=20 X(k) when delta is tiny. If delta is not sufficiently small, the relationsh= ip=20 may not be clear.        &nb= sp; =20      &nb= sp; A more=20 general problem about sensitivity analysis of solutions=20 to  polynomial systems is discussed in one of our papers.  The following paper may be use= ful to=20 you:
           = =20  
http://front.math.ucdavis.edu/math.OC/0411122
Given a multivariate system of polynomial= s=20 p(x,mu), where the mu's can  be thought of as parameters determining t= he=20 coefficient of p(), we give an algorithm  for computing the minimal=20 ellipsoid contining all the real solutions x of p(x,mu)=3D0.  For exam= ple, if=20 q() is a single polynomial in the scalar x with coefficients in
interva= ls=20 with given centers and radii, and you want bounds on the real zeros,then th= is=20 can be formulated as finding  the minimum ellipsoid containing the&nbs= p;=20 roots x of a system like

      sum_{i=3D0 t= o=20 n}   mu_i * x^i  =3D 0
      (mu= _i -=20 center_i)^2 + mu'_i^2 =3D radius^2   for  i =3D 0 to n
The=20 paper uses techniques from semidefinite=20 programming.

Regards,
Jiawang Nie and Jim=20 Demmel

----- Original Message ----- Fro= m:=20 Patrizia= =20 Lamberti To: reliable_comput= ing [at] interval [dot] louisiana.edu=20 Sent: Wednesday, January = 12, 2005 6:59=20 AM Subject: polynomial varia= bility

I am a PhD Student in Information and= =20 Electric Engineering at the=20 University of=20 Salerno,=20 Italy.

 

I am investigating the possibility of determinin= g the=20 range of minimum variability of a polynomial by means of interval=20 analysis.

 

I prefer to describe the problem by using a simp= le=20 example.

 

Let us consider the 5th ord= er=20 polynomial f(x)=3Dx^5+60*x^4+30*x^3-10*x^2+6, which has 2 minima and 3 ma= xima in=20 the range I=3D[-1.0,0.7]. Let us inspect the behaviour of f over I by=20 considering a translating WIDE interval X(k)=3D[x0(k)-delta,x0(k)+delta],= =20 included in I, with x0=3D{-0.7,-0.6,=85,0.3,0.4} and delta=3D0.3. Let us = calculate=20 the Taylor expansion of f(x) centre= d in=20 x0(k), k=3D1,2,=85, and evaluate its interval extension=20 F_TM(X(k)).

I have found that, among the N values F_TM(X(k))= =20 calculated, the one of minimum radius is obtained for the X(k) wherein th= e=20 real function f(x) is subjected to the minimum variation (namely, in that= X(k)=20 the united extension of f(X(k)) assumes the minimum=20 radius).

 

Note that:

1)     =20 the F_TM(X(k)) are calc= ulated=20 over intervals X(k) of fixed, and big, amplitude=20 2*delta;

2)     =20 I don=92t have looked f= or the true=20 range of f over I or X(k), but I it was enough for me to look for the ran= ge of=20 minimum (even if unknown) radius of=20 f(x).

 

Now, I have some=20 questions:

1)     =20 is this result of gener= al=20 validity, namely for any polynomial and/or function in general? Does it e= xist=20 some theorem helpful to demonstrate it in=20 general?

2)     =20 has this problem alread= y=20 afforded in literature?

 

Please, do not hesitate to ask for further=20 details.

 

Best=20 regards

 

Patrizia=20 Lamberti

 

------=_NextPart_000_0019_01C4F8AA.66FEA630-- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 12 17:03:37 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0CN3aEs014528 for ; Wed, 12 Jan 2005 17:03:36 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0CN3aMm014527 for reliable_computing-outgoing; Wed, 12 Jan 2005 17:03:36 -0600 (CST) Received: from lakermmtao05.cox.net (lakermmtao05.cox.net [68.230.240.34]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0CN3PXM014523 for ; Wed, 12 Jan 2005 17:03:32 -0600 (CST) Received: from Inspiron-8200 ([68.226.133.93]) by lakermmtao05.cox.net (InterMail vM.6.01.04.00 201-2131-117-20041022) with SMTP id <20050112230319.XBHY16431.lakermmtao05.cox.net@Inspiron-8200>; Wed, 12 Jan 2005 18:03:19 -0500 Message-Id: <2.2.32.20050112230307.00a02a40 [at] pop [dot] louisiana.edu> X-Sender: rbk5287 [at] pop [dot] louisiana.edu X-Mailer: Windows Eudora Pro Version 2.2 (32) Mime-Version: 1.0 Content-Type: multipart/mixed; boundary="=====================_1105592587==_" Date: Wed, 12 Jan 2005 17:03:07 -0600 To: "Jiawang Nie" , "Patrizia Lamberti" , From: "R. Baker Kearfott" Subject: Re: polynomial variability Cc: "James Demmel" X-Attachments: C:\baker\miscellaneous_GlobSol_experiments\2005_01_12_Lam bert.f90; C:\baker\miscellaneous_GlobSol_experiments\2005_01_12_Lambert.DT1; C:\baker\miscellaneous_GlobSol_experiments\2005_01_12_Lambert.OT1; Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000030 --=====================_1105592587==_ Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable All, For that matter, GlobSol has no problems finding facts about this particular univariate polynomial=20 (roots, minima, maxima, critical points, etc.). For example, I've attached GlobSol input and output files for finding the minimum (validated) over the interval Patrizia=20 specified. Best regards, Baker At 01:27 PM 1/12/2005 -0800, Jiawang Nie wrote: > >Dear Patrizia: > > Your question about polynomial variability is very interesting, and related to our work.=20 > > The global minimum or maximum of a univariate polynomial on an interval [a,b] can be found very efficiently by software SOSTOOLS or Gloptipoly ( search in google for the references and websits). So the true range of f(x) over your X(k) can be found.=20 > > The interval extensions F_TM(X(k)) evaluated via taylor expansion ( first order ?) of f(x) reflect the true range of f(x) over X(k) when delta is tiny. If delta is not sufficiently small, the relationship may not be= clear. > > =20 > A more general problem about sensitivity analysis of solutions to polynomial systems is discussed in one of our papers. The following paper may be useful to you: > http://front.math.ucdavis.edu/math.OC/0411122 >Given a multivariate system of polynomials p(x,mu), where the mu's can be thought of as parameters determining the coefficient of p(), we give an algorithm for computing the minimal ellipsoid contining all the real solutions x of p(x,mu)=3D0. For example, if q() is a single polynomial in= the scalar x with coefficients in=20 >intervals with given centers and radii, and you want bounds on the real zeros,then this can be formulated as finding the minimum ellipsoid containing the roots x of a system like > > sum_{i=3D0 to n} mu_i * x^i =3D 0 > (mu_i - center_i)^2 + mu'_i^2 =3D radius^2 for i =3D 0 to n > >The paper uses techniques from semidefinite programming. > > >Regards, >Jiawang Nie and Jim Demmel > > ----- Original Message -----=20 > From: Patrizia Lamberti=20 > To: reliable_computing [at] interval [dot] louisiana.edu=20 > Sent: Wednesday, January 12, 2005 6:59 AM > Subject: polynomial variability > > > I am a PhD Student in Information and Electric Engineering at the University of Salerno, Italy. > > =20 > > I am investigating the possibility of determining the range of minimum variability of a polynomial by means of interval analysis. > > =20 > > I prefer to describe the problem by using a simple example. > > =20 > > Let us consider the 5th order polynomial f(x)=3Dx^5+60*x^4+30*x^3-10*x^2+= 6, which has 2 minima and 3 maxima in the range I=3D[-1.0,0.7]. Let us inspect the behaviour of f over I by considering a translating WIDE interval X(k)=3D[x0(k)-delta,x0(k)+delta], included in I, with= x0=3D{-0.7,-0.6,.,0.3,0.4} and delta=3D0.3. Let us calculate the Taylor expansion of f(x) centred in x0(k), k=3D1,2,., and evaluate its interval extension F_TM(X(k)). > > I have found that, among the N values F_TM(X(k)) calculated, the one of minimum radius is obtained for the X(k) wherein the real function f(x) is subjected to the minimum variation (namely, in that X(k) the united extension of f(X(k)) assumes the minimum radius). > > =20 > > Note that: > > 1) the F_TM(X(k)) are calculated over intervals X(k) of fixed, and big, amplitude 2*delta; > > 2) I don't have looked for the true range of f over I or X(k), but I it was enough for me to look for the range of minimum (even if unknown) radius of f(x). > > =20 > > Now, I have some questions: > > 1) is this result of general validity, namely for any polynomial and/or function in general? Does it exist some theorem helpful to demonstrate it in general? > > 2) has this problem already afforded in literature? > > =20 > > Please, do not hesitate to ask for further details. > > =20 > > Best regards > > =20 > > Patrizia Lamberti > > =20 > >"urn:schemas-microsoft-com:office:office"> > > > > > > >  >Dear  Patrizia: >  >     = Your question about=20 >polynomial variability is very interesting, and related to our work.=20 > >  >     = The global minimum=20 >or maximum of a univariate polynomial on an interval [a,b] can be found= very=20 >efficiently by software SOSTOOLS or Gloptipoly ( search in google for the= =20 >references and websits). So the true range of f(x)  over your X(k) can= be=20 >found. >  >     = The interval=20 >extensions F_TM(X(k)) evaluated via= taylor=20 >expansion ( first order ?) of  f(x) reflect the true range of f(x)= over=20 >X(k) when delta is tiny. If delta is not sufficiently small, the= relationship=20 >may not be clear. >  >       =20 > >       A more=20 >general problem about sensitivity analysis of solutions=20 >to  polynomial systems is discussed in one of our papers.face=3D"Times New Roman" size=3D3>  The size=3D2>following paper may be= useful to=20 >you:
           = =20 > 
size=3D3>http://front.math.ucdavis.edu/math.OC/0411122
face=3D"Times New Roman" size=3D3>Given a multivariate system of= polynomials=20 >p(x,mu), where the mu's can  be thought of as parameters determining= the=20 >coefficient of p(), we give an algorithm  for computing the minimal=20 >ellipsoid contining all the real solutions x of p(x,mu)=3D0.  For example, if=20 >q() is a single polynomial in the scalar x with coefficients in=
intervals=20 >with given centers and radii, and you want bounds on the real zeros,then= this=20 >can be formulated as finding  the minimum ellipsoid containing= the =20 >roots x of a system like

      sum_{i=3D0= to=20 >n}   mu_i * x^i  =3D 0
     = (mu_i -=20 >center_i)^2 + mu'_i^2 =3D radius^2   for  i =3D 0 to= n

The=20 >paper uses techniques from semidefinite=20 >programming.
face=3D"Times New Roman" size=3D3> >
Regards,
Jiawang Nie and Jim=20 >Demmel

>
DEFANGED_style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> > ----- Original Message ----- > style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black">From:=20 > Patrizia= =20 > Lamberti > To: title=3Dreliable_computing [at] interval [dot] louisiana.edu=20 > href=3D"mailto:reliable_computing [at] interval [dot] louisiana.edu">reliable_computing= @i nterval.louisiana.edu=20 > > Sent: Wednesday, January 12, 2005 6:59=20 > AM > Subject: polynomial variability >
face=3DArial size=3D2> >

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"> face=3D"Times New Roman"> style=3D"mso-ansi-language: EN-GB">I am a PhD Student in Information and= =20 > Electric Engineering at the=20 > = lang=3DEN-GB=20 > style=3D"mso-ansi-language: EN-GB">University lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> of=20 > style=3D"mso-ansi-language: EN-GB">Salerno lang=3DEN-GB style=3D"mso-ansi-language: EN-GB">,=20 > lang=3DEN-GB=20 > style=3D"mso-ansi-language: EN-GB">Italy lang=3DEN-GB=20 > style=3D"mso-ansi-language: EN-GB">.

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> size=3D3> 

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> face=3D"Times New Roman">I am investigating the possibility of= determining the=20 > range of minimum variability of a polynomial by means of interval=20 > analysis.

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> size=3D3> 

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> face=3D"Times New Roman">I prefer to describe the problem by using a= simple=20 > example.

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> size=3D3> 

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"> face=3D"Times New Roman"> style=3D"mso-ansi-language: EN-GB">Let us consider the 5th= order=20 > polynomial f(x)=3Dx^5+60*x^4+30*x^3-10*x^2+6, which has 2 minima and 3 maxima in=20 > the range I=3D[-1.0,0.7]. Let us inspect the behaviour of f over I by=20 > considering a translating WIDE interval X(k)=3D[x0(k)-delta,x0(k)+delta],= =20 > included in I, with x0=3D{-0.7,-0.6,=85,0.3,0.4} and delta=3D0.3. Let us= calculate=20 > the lang=3DEN-GB=20 > style=3D"mso-ansi-language: EN-GB">Taylor lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> expansion of f(x)= centred in=20 > x0(k), k=3D1,2,=85, and evaluate its interval extension=20 > F_TM(X(k)).

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> face=3D"Times New Roman">I have found that, among the N values F_TM(X(k))= =20 > calculated, the one of minimum radius is obtained for the X(k) wherein= the=20 > real function f(x) is subjected to the minimum variation (namely, in that X(k)=20 > the united extension of f(X(k)) assumes the minimum=20 > radius).

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> size=3D3> 

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> face=3D"Times New Roman">Note that:

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt 36pt; TEXT-INDENT: -18pt;= TEXT-ALIGN: justify; mso-list: l1 level1 lfo1; tab-stops: list 36.0pt"> face=3D"Times New Roman"> style=3D"mso-ansi-language: EN-GB"> size=3D3>1) style=3D"FONT: 7pt 'Times New Roman'">     =20 > style=3D"mso-ansi-language: EN-GB">the F_TM(X(k)) are= calculated=20 > over intervals X(k) of fixed, and big, amplitude=20 > 2*delta;

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt 36pt; TEXT-INDENT: -18pt;= TEXT-ALIGN: justify; mso-list: l1 level1 lfo1; tab-stops: list 36.0pt"> face=3D"Times New Roman"> style=3D"mso-ansi-language: EN-GB"> size=3D3>2) style=3D"FONT: 7pt 'Times New Roman'">     =20 > style=3D"mso-ansi-language: EN-GB">I don=92t have looked= for the true=20 > range of f over I or X(k), but I it was enough for me to look for the range of=20 > minimum (even if unknown) radius of=20 > f(x).

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> size=3D3> 

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> face=3D"Times New Roman">Now, I have some=20 > questions:

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt 36pt; TEXT-INDENT: -18pt;= TEXT-ALIGN: justify; mso-list: l0 level1 lfo2; tab-stops: list 36.0pt"> face=3D"Times New Roman"> style=3D"mso-ansi-language: EN-GB"> size=3D3>1) style=3D"FONT: 7pt 'Times New Roman'">     =20 > style=3D"mso-ansi-language: EN-GB">is this result of= general=20 > validity, namely for any polynomial and/or function in general? Does it exist=20 > some theorem helpful to demonstrate it in=20 > general?

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt 36pt; TEXT-INDENT: -18pt;= TEXT-ALIGN: justify; mso-list: l0 level1 lfo2; tab-stops: list 36.0pt"> face=3D"Times New Roman"> style=3D"mso-ansi-language: EN-GB"> size=3D3>2) style=3D"FONT: 7pt 'Times New Roman'">     =20 > style=3D"mso-ansi-language: EN-GB">has this problem= already=20 > afforded in literature?

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt 18pt; TEXT-ALIGN: justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> size=3D3> 

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> face=3D"Times New Roman">Please, do not hesitate to ask for further=20 > details.

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> size=3D3> 

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> face=3D"Times New Roman">Best=20 > regards

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> size=3D3> 

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> face=3D"Times New Roman">Patrizia=20 > Lamberti

>

DEFANGED_style=3D"MARGIN: 0cm 0cm 0pt; TEXT-ALIGN:= justify"> lang=3DEN-GB style=3D"mso-ansi-language: EN-GB"> size=3D3> 

> --=====================_1105592587==_ Content-Type: text/plain; charset="us-ascii" Content-Disposition: attachment; filename="2005_01_12_Lambert.f90" ! Return-Path: ! From: "Patrizia Lamberti" ! To: ! Subject: polynomial variability ! Date: Wed, 12 Jan 2005 15:59:09 +0100 ! Sender: owner-reliable_computing [at] interval [dot] louisiana.edu ! ! I am a PhD Student in Information and Electric Engineering at ! the University of Salerno, Italy. ! ! ! ! I am investigating the possibility of determining the range of ! minimum variability of a polynomial by means of interval ! analysis. ! ! ! ! I prefer to describe the problem by using a simple example. ! ! ! ! Let us consider the 5th order polynomial ! f(x)=x^5+60*x^4+30*x^3-10*x^2+6, which has 2 minima and 3 maxima ! in the range I=[-1.0,0.7]. Let us inspect the behaviour of f ! over I by considering a translating WIDE interval ! X(k)=[x0(k)-delta,x0(k)+delta], included in I, with ! x0={-0.7,-0.6,.,0.3,0.4} and delta=0.3. Let us calculate the ! Taylor expansion of f(x) centred in x0(k), k=1,2,., and evaluate ! its interval extension F_TM(X(k)). ! ! I have found that, among the N values F_TM(X(k)) calculated, ! the one of minimum radius is obtained for the X(k) wherein the ! real function f(x) is subjected to the minimum variation ! (namely, in that X(k) the united extension of f(X(k)) assumes ! the minimum radius). ! ! ! ! Note that: ! 1) the F_TM(X(k)) are calculated over intervals X(k) of fixed, ! and big, amplitude 2*delta; ! 2) I don't have looked for the true range of f over I or X(k), ! but I it was enough for me to look for the range of minimum ! (even if unknown) radius of f(x). ! ! ! ! Now, I have some questions: ! 1) is this result of general validity, namely for any ! polynomial and/or function in general? Does it exist some ! theorem helpful to demonstrate it in general? ! ! 2) has this problem already afforded in literature? ! ! ! ! Please, do not hesitate to ask for further details. ! ! ! !Best regards ! ! !Patrizia Lamberti PROGRAM LAMBERT_2005_01_12 USE CODELIST_CREATION TYPE(CDLVAR), DIMENSION(1):: X TYPE(CDLLHS), DIMENSION(1):: PHI CALL INITIALIZE_CODELIST(X) PHI(1) = X(1)**5 + 60*X(1)**4 + 30*X(1)**3 - 10*X(1)**2 + 6 CALL FINISH_CODELIST END PROGRAM LAMBERT_2005_01_12 --=====================_1105592587==_ Content-Type: text/plain; charset="us-ascii" Content-Disposition: attachment; filename="2005_01_12_Lambert.DT1" 1D-10 -1 0.7 T T --=====================_1105592587==_ Content-Type: text/plain; charset="us-ascii" Content-Disposition: attachment; filename="2005_01_12_Lambert.OT1" Output from FIND_GLOBAL_MIN on 01/12/2005 at 16:58:39. Version for the system is: November 22, 2003 Codelist file name is: 2005_01_12_LambertG.CDL Box data file name is: 2005_01_12_Lambert.DT1 Initial box: [ -0.1000D+01, 0.7000D+00 ] BOUND_CONSTRAINT: T T --------------------------------------- CONFIGURATION VALUES: EPS_DOMAIN: 0.1000D-09 MAXITR: 100000 MAX_CPU_SECONDS: 0.3600D+04 MAX_LP_PRE: 500 DO_INTERVAL_NEWTON: T QUADRATIC: T FULL_SPACE: F VERY_GOOD_INITIAL_GUESS: F USE_SUBSIT: T OUTPUT UNIT: 7 PRINT_LENGTH: 1 PHI_MUST_CONVERGE: T EQ_CNS_MUST_CONVERGE: T INEQ_CNS_MUST_CONVERGE: T PHI_THICKNESS_FACTOR: 0.5000D+00 EQ_CNS_THICKNESS_FACTOR: 0.5000D+00 INEQ_CNS_THICKNESS_FACTOR: 0.5000D+00 PHI_MUST_CONVERGE: T EQ_CNS_MUST_CONVERGE: T INEQ_CNS_MUST_CONVERGE: T PHI_CONVERGENCE_FACTOR: 0.1000D-13 EQ_CNS_CONVERGENCE_FACTOR: 0.1000D-13 INEQ_CNS_CONVERGENCE_FACTOR: 0.1000D-13 CONTINUITY_ACROSS_BRANCHES: F SINGULAR_EXPANSION_FACTOR: 0.1000D+02 HEURISTIC PARAMETER ALPHA: 0.5000D+00 APPROX_OPT_BEFORE_BISECTION: F APPROX_OPTIMIZER_TYPE 1 USE_LP: F ITERATE__LP: F EPS_LP_FIT: 0.100000000000000 USE_EPPERLY_SPLIT: 0 PRINTING_IN_SPLIT 0 USE_REDUCED_SPACE: F USE_TAYLOR_EQUALITY_CONSTRAINTS F USE_TAYLOR_INEQ_CONSTRAINTS F USE_TAYLOR_OBJECTIVE F USE_TAYLOR_EQ_CNS_GRD F USE_TAYLOR_GRAD F USE_TAYLOR_INEQ_CNS_GRD F USE_TAYLOR_REDUCED_INEWTON T COSY_POLYNOMIAL_ORDER 5 LEAST_SQUARES_FUNCTIONS: F NONLINEAR_SYSTEM: F DO_PIVOTING: F DO_INV_MID: F TRY_C_LP_HEURISTIC: 10000000000.0000 Success in initial location of an approximate optimum feasible_region returned: [ -0.1501D+00, -0.1499D+00 ] after the interval Newton method, APPROX_OPT_BOX Box coordinates: [ -0.1501D+00, -0.1499D+00 ] PHI: [ 0.5704D+01, 0.5704D+01 ] B%LIUI(1,*): F B%LIUI(2,*): F B%SIDE(*): F B%PEEL(*): F Level: 0 Box contains the following approximate root: -0.1500D+00 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.5704D+01, 0.5704D+01 ] Unknown = T Contains_root = T Changed coordinates: F After PEEL_BOUNDARY, number of boxes in current_list: 1 After COMPLEMENT_LIST, number of boxes in current_list: 2 C_LP_WITH_DSPLP, version corresponding to the original 1990 SIAM preconditioner computation, was used to compute LP preconditioners. THERE WERE NO BOXES IN THE LIST OF SMALL BOXES. LIST OF BOXES CONTAINING VERIFIED FEASIBLE POINTS: Box no.: 1 Box coordinates: [ -0.5364D+00, -0.5364D+00 ] PHI: [ 0.3415D+01, 0.3415D+01 ] B%LIUI(1,*): F B%LIUI(2,*): F B%SIDE(*): F B%PEEL(*): T Level: 1 Box contains the following approximate root: -0.5364D+00 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.3415D+01, 0.3415D+01 ] Unknown = T Contains_root = T Changed coordinates: T ------------------------------------------------- ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 100000 OF BOXES. Number of bisections: 3 No. dense interval residual evaluations -- gradient code list: 78 Number of orig. system C-LP preconditioner rows: 6 Number of solutions for a component in the expanded system: 1242 Total number of forward_substitutions: 166 Number of Gauss--Seidel steps on the dense system: 5 Number of gradient evaluations from a gradient code list: 18 Total number of dense slope matrix evaluations: 29 Total number second-order interval evaluations of the original function: 21 Total number dense interval reduced gradient evaluations: 19 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 1 Total time spent doing linear algebra (preconditioners and solution processes): 1.001440000000000E-002 Time spent computing LP preconditioners: 1.001440000000000E-002 Average number of overall loop iterations in each call to the reduced interval Newton method): 1.57142857142857 Number of times a box was rejected in the interval Newton method due to an empty intersection: 1 Number of times the interval Newton method made a coordinate interval smaller: 4 Total number of times the reduced interval Newton method was tried: 7 Number of times a C LP preconditioner led to improvement or rejection: 5 Number of times a C LP preconditioner failed to improve or reject: 3 Number of times the approximate solver was called: 3 Number Fritz-John matrix evaluations: 8 Number of times SUBSIT decreased one or more coordinate widths: 2 Number of times SUBSIT rejected a box: 1 Total number of boxes processed in loop: 6 Number of times solving an LP with DSPLP was successful: 3 Number of times solving an LP with DSPLP failed: 3 BEST_ESTIMATE: 0.3415D+01 Overall CPU time: 0.2003D-01 CPU time in PEEL_BOUNDARY: 0.0000D+00 CPU time in REDUCED_INTERVAL_NEWTON: 0.1001D-01 --=====================_1105592587==_ Content-Type: text/plain; charset="us-ascii" --------------------------------------------------------------- R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax) (337) 482-5270 (work) (337) 993-1827 (home) URL: http://interval.louisiana.edu/kearfott.html Department of Mathematics, University of Louisiana at Lafayette (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) Box 4-1010, Lafayette, LA 70504-1010, USA --------------------------------------------------------------- --=====================_1105592587==_-- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 12 23:36:52 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0D5ap53015134 for ; Wed, 12 Jan 2005 23:36:51 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0D5apos015133 for reliable_computing-outgoing; Wed, 12 Jan 2005 23:36:51 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0D5agqf015129 for ; Wed, 12 Jan 2005 23:36:48 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j0D5aSl16788; Wed, 12 Jan 2005 22:36:28 -0700 (MST) Message-Id: <200501130536.j0D5aSl16788 [at] cs [dot] utep.edu> Date: Wed, 12 Jan 2005 22:36:29 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Postdoctoral Position at INRIA/Ecole Normale Superieure, Lyon: from NA DIgest To: reliable_computing [at] interval [dot] louisiana.edu Cc: Gilles.Villard@ens-lyon.fr MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: uBFS0bZbkrOFtgMdSKJ+HA== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000031 Apologies for multiple copies; please notice that interval arithmetic is explicitly mentioned *********************************************************************** From: Gilles Villard POSTDOCTORAL POSITION IN COMPUTER SCIENCE, DIGITAL SIGNATURE AND HARDWARE ARITHMETIC OPERATORS, INRIA/ECOLE NORMALE SUPERIEURE, LYON FRANCE Arnaud Tisserand and Gilles Villard {Arnaud.Tisserand,Gilles.Villard}@ens-lyon.fr Arnaire project http://www.ens-lyon.fr/LIP/Arenaire (CNRS/ENSL/INRIA/UCBL) Laboratoire LIP, cole Normale Suprieure, 46 Alle d'Italie, 69364 Lyon Cedex 07 France The INRIA project Arenaire offers a 12 months postdoc position starting as soon as possible. Objectives Last years have seen major investments in public-key cryptography research. Indeed, new commercial cryptographic products rely on very high ciphering speed. The efficiency of cryptographic algorithms is a crucial issue nowadays, and the design of hardware implementations is an important point for providing new solutions. In collaboration with several other groups (ACI Securite Informatique --- http://www-rocq.inria.fr/codes/OCAM), the objective of the postdoc is to participate to the development of a FPGA-based PC board prototype for digital signature. Together with the development of an experimental platform for best software and hardware solutions comparizon, the goal is to offer a complete hardware demonstrator usable by any standard computer. Work directions may concern FPGA programming, elaboration of test programs, data communication and system aspects. A joint research project of the candidate may be around cryptography, low-power hardware, or hardware for computer arithmetic. Arnaire project. Arnaire is a project of 16 researchers which aims at elaborating and consolidating knowledge in the field of computer arithmetic. We contribute to the improvement of the available arithmetic, at the hardware level as well as at the software level, on computers, processors, dedicated or embedded chips, etc. Reliability, accuracy, and speed are major goals that drive our studies. We also take into account other constraints such as power consumption, certification using formal proof techniques or reliability of numerical software. Target arithmetics are fixed or floating point format, interval arithmetic, finite fields arithmetic and multiple precision. Skills and application Knowledge in hardware design, for instance using VHDL for FPGAs, and in the domain of cryptographic algorithms will be appreciated. Interested candidates should contact or send files directly to {Arnaud.Tisserand, Gilles.Villard}@ens-lyon.fr as soon as possible. Files must contain a cv, a brief description of research work and recommendation letters. From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 12 23:46:42 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0D5kgpg015252 for ; Wed, 12 Jan 2005 23:46:42 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0D5kg3n015251 for reliable_computing-outgoing; Wed, 12 Jan 2005 23:46:42 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0D5kY8H015247 for ; Wed, 12 Jan 2005 23:46:39 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j0D5kQ716826 for ; Wed, 12 Jan 2005 22:46:26 -0700 (MST) Message-Id: <200501130546.j0D5kQ716826 [at] cs [dot] utep.edu> Date: Wed, 12 Jan 2005 22:46:27 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: ISSAC 2005: deadline extended To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: KYKiy2HFCodXKePc54Jjjw== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000032 forwarding ------------- Begin Forwarded Message ------------- Date: Wed, 12 Jan 2005 12:24:18 +0800 From: ISSAC 2005 ISSAC2005 Call for Papers Third Announcement International Symposium on Symbolic and Algebraic Computation July 24-27, 2005, Beijing, China. http://www.mmrc.iss.ac.cn/issac2005/ ********************************************************************* The deadline for submission of papers to ISSAC 2005 has been extended to January 21, 2005 (Midnight [24:00 EST]). Paper Submission Webpage: https://issac2005.risc.uni-linz.ac.at/ ********************************************************************* ISSAC2005 program consists of Contributed Talks Poster Presentations Software Exhibitions Invited Talks Bruno Buchberger, RISC-Linz, Austria Bruno Salvy, INRIA, France Wen-Tsun Wu, Chinese Academy of Sciences, China Tutorials Evelyne Hubert INRIA, Sophia Antipolis, France Arnaud Tisserand INRIA, Lyon, France Jan Verschelde University of Chicago, USA Satellite Workshops Algebraic Methods in Cryptography Internet Accessible Mathematical Computation Symbolic-Numeric Computation Distinguished Paper Award and Distinguished Student Author Award will be selected. ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Jan 13 10:01:23 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0DG1NkX016445 for ; Thu, 13 Jan 2005 10:01:23 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0DG1MDF016444 for reliable_computing-outgoing; Thu, 13 Jan 2005 10:01:22 -0600 (CST) Received: from baobab.unisa.it (baobab.unisa.it [193.205.160.136]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0DG1Bqv016440 for ; Thu, 13 Jan 2005 10:01:19 -0600 (CST) Received: from plportatile (niki.diiie.unisa.it [193.205.164.127]) by baobab.unisa.it (8.13.2/8.13.2) with SMTP id j0DG0U3L188898 for ; Thu, 13 Jan 2005 17:00:40 +0100 (CET) Message-ID: <019501c4f989$0b7e9f60$7fa4cdc1@plportatile> From: "Patrizia Lamberti" To: Subject: re: polynomial variability Date: Thu, 13 Jan 2005 17:00:31 +0100 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0192_01C4F991.63DABBF0" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Spam-Score: (-1.424) BAYES_01,HTML_MESSAGE X-Scanned-By: MIMEDefang 2.42 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: RO X-Status: $$$$ X-UID: 0000000033 This is a multi-part message in MIME format. ------=_NextPart_000_0192_01C4F991.63DABBF0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Dear prof. Kearfott, Demmel and Jiawang Nie, thank you very much for your prompt reply. I am afraid I was not very clear in the description of the problem. Indeed, my objective is NOT the accurate evaluation of the exact range = of the polynomial. Instead I am looking for an approach that gives me = information about where the region of minimum variability of the = function is located. To this aim, it is enough for me that the = overestimation of the united extension is the minimum in the interval = wherein the function shows the lowest sensitivity. Note that it is = enough to know that we have THERE the minimum overestimation with = respect to the overestimation obtained for the interval of the same = width, but centered in any other point. Note that the range I look for may not to be coincident with a = minimum/maximum of the function f(x). If the amplitude of the united = extension f(X(k)) is w(f(X(k)))=3Dmax(f(X(k)))-min(f(X(k))), we are = looking for the X(k) to which corresponds the minimum w(f(X(k))). That = is the region of minimum variability. Now, I was trying an interval extension F(X(k)) of f(x) on the interval = X(k) such that w(F(X(k))) had the same behaviour of w(f(X(k))). In = particular that w(F(X(k))) was minimum just where w(f(X(k))) was, even = if w(F(X(k)))>> w(f(X(k))). Actually, using the Taylor Model of f as interval extension = (F_TM(X(k))), i.e. by using the complete Taylor series of f(x) around = x0(k) and estimating it in terms of interval variable, I have verified = that w(F(X(k))) keeps the presence of local and absolute minima just = where local and absolute minima of w(f(X(k))) are. In particular it is = true for a generic parabola and for all the polynomials that I have = randomly obtained (from 3rd to 9th order). Moreover this characteristic = is maintained for all delta, i.e. both tight and wide interval. I think improbable that these are only coincidences, rather I'm looking = for a justification to this behaviour in the properties of the Taylor = Model. Can you help me about this topics? May this result be extended to any = polynomial function? Are there some theorems about this? I have not found a precise reference to this topic in literature, but I = am afraid I am not searching for in the right way. I am sure that you = can address me in the right way. At the best of your knowledge, is somewhere anyone who has been = interested in the region of minimum w(f(X(k))) rather than the minimum = of f(X(k)), or the best inclusion of the function? Do you think that the use of TM is valid or suggest alternatives to me? Thanks in advance Patrizia Lamberti ------=_NextPart_000_0192_01C4F991.63DABBF0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Dear prof. Kearfott, Demmel and Jiawang Nie,

thank you very = much for=20 your prompt reply.

I am afraid I was not very clear in the = description of=20 the problem.
Indeed, my objective is NOT the accurate evaluation of the exact = range of=20 the polynomial. Instead I am looking for an approach that gives me = information=20 about where the region of minimum variability of the function is = located. To=20 this aim, it is enough for me that the overestimation of the united = extension is=20 the minimum in the interval wherein the function shows the lowest = sensitivity.=20 Note that it is enough to know that we have THERE the minimum = overestimation=20 with respect to the overestimation obtained for the interval of the same = width,=20 but centered in any other point.

Note that the range I look for = may not=20 to be coincident with a minimum/maximum of the function f(x). If the = amplitude=20 of the united extension f(X(k)) is = w(f(X(k)))=3Dmax(f(X(k)))-min(f(X(k))), we are=20 looking for the X(k) to which corresponds the minimum w(f(X(k))). That = is the=20 region of minimum variability.

Now, I was trying an interval = extension=20 F(X(k)) of f(x) on the interval X(k) such that w(F(X(k))) had the same = behaviour=20 of w(f(X(k))). In particular that w(F(X(k))) was minimum just where = w(f(X(k)))=20 was, even if w(F(X(k)))>> w(f(X(k))).

Actually, using the = Taylor=20 Model of f as interval extension (F_TM(X(k))), i.e. by using the = complete Taylor=20 series of f(x) around x0(k) and estimating it in terms of interval = variable, I=20 have verified that w(F(X(k))) keeps the presence of local and absolute = minima=20 just where local and absolute minima of w(f(X(k))) are. In particular it = is true=20 for a generic parabola and for all the polynomials that I have randomly = obtained=20 (from 3rd to 9th order). Moreover this characteristic is maintained for = all=20 delta, i.e. both tight and wide interval.

I think improbable that = these=20 are only coincidences, rather I'm looking for a justification to this = behaviour=20 in the properties of the Taylor Model.
Can you help me about this topics? May this result be extended to = any=20 polynomial function? Are there some theorems about this?

I have = not found=20 a precise reference to this topic in literature, but I am afraid I am = not=20 searching for in the right way. I am sure that you can address me in the = right=20 way.

At the best of your knowledge, is somewhere anyone who has = been=20 interested in the region of minimum w(f(X(k))) rather than the minimum = of=20 f(X(k)), or the best inclusion of the function?

Do you think that = the use=20 of TM is valid or suggest alternatives to me?

Thanks in=20 advance

Patrizia Lamberti
------=_NextPart_000_0192_01C4F991.63DABBF0-- From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Jan 13 11:17:22 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0DHHLSY016669 for ; Thu, 13 Jan 2005 11:17:21 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0DHHLSM016668 for reliable_computing-outgoing; Thu, 13 Jan 2005 11:17:21 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0DHHJan016664 for ; Thu, 13 Jan 2005 11:17:19 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0DHHIhD016663 for reliable_computing [at] interval [dot] louisiana.edu; Thu, 13 Jan 2005 11:17:18 -0600 (CST) Received: from fw.cs.cas.cz (IDENT:root [at] fw [dot] cs.cas.cz [147.231.6.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0D9UT8x015661 for ; Thu, 13 Jan 2005 03:30:43 -0600 (CST) Received: (from mailprox@localhost) by fw.cs.cas.cz (8.11.5/8.11.5) id j0D9UR016334 for ; Thu, 13 Jan 2005 10:30:27 +0100 X-Authentication-Warning: fw.cs.cas.cz: mailprox set sender to SIZE=990 using -f Received: from uivt1.cs.cas.cz(147.231.4.1) by fw.cs.cas.cz via smap (V2.1/2.1+anti-relay+anti-spam) id xmaa16327; Thu, 13 Jan 05 10:30:26 +0100 Received: from uivt1.cs.cas.cz (localhost.localdomain [127.0.0.1]) by uivt1.cs.cas.cz (8.12.10/8.12.8) with ESMTP id j0D9UQiR029216 for ; Thu, 13 Jan 2005 10:30:26 +0100 Received: (from nobody@localhost) by uivt1.cs.cas.cz (8.12.10/8.12.10/Submit) id j0D9UQKA029214; Thu, 13 Jan 2005 10:30:26 +0100 X-Authentication-Warning: uivt1.cs.cas.cz: nobody set sender to rohn [at] cs [dot] cas.cz using -f Received: from 147.231.4.31 (SquirrelMail authenticated user rohn); by www.cs.cas.cz with HTTP; Thu, 13 Jan 2005 10:30:26 +0100 (CET) Message-ID: <4137.147.231.4.31.1105608626.squirrel [at] 147 [dot] 231.4.31> Date: Thu, 13 Jan 2005 10:30:26 +0100 (CET) Subject: change of address From: "Jiri Rohn" To: reliable_computing [at] interval [dot] louisiana.edu User-Agent: SquirrelMail/1.4.3a-0.f1.1 X-Mailer: SquirrelMail/1.4.3a-0.f1.1 MIME-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Priority: 3 (Normal) Importance: Normal Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000034 Dear colleagues, Please note my new address: Institute of Computer Science Pod vodarenskou vezi 2 182 07 Prague Czech Republic e-mail: rohn [at] cs [dot] cas.cz With best wishes, Jiri Rohn From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Jan 13 22:19:46 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0E4JkOx017451 for ; Thu, 13 Jan 2005 22:19:46 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0E4JkNg017450 for reliable_computing-outgoing; Thu, 13 Jan 2005 22:19:46 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0E4JbZu017446 for ; Thu, 13 Jan 2005 22:19:43 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j0E4JTd24269; Thu, 13 Jan 2005 21:19:29 -0700 (MST) Message-Id: <200501140419.j0E4JTd24269 [at] cs [dot] utep.edu> Date: Thu, 13 Jan 2005 21:19:29 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Engineering Reliability Design Handbook has been published To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu Cc: enikolai [at] eng [dot] utoledo.edu, rafi.muhanna [at] gtrep [dot] gatech.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: PQjr59M69xmB1aw606Cjbw== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000035 Dear Vladik, Our community might be interested in the book, Rafi Muhanna and Robert Mullen have a chapter entitled "Interval Methods for Reliable computing"; several other chapters are relevant *************************************************************************** Efstratios Nikolaidis, Dan Ghiocel, and Suren Singhal recently edited the CRC Engineering Reliability Design Handbook. This book was published in December 2004. The handbook contains 45 chapters written by well-respected experts from government labs, companies and universities. The book contents include methods for uncertainty quantification using probabilistic and non probabilistic approaches, computational methods for reliability assessment, reliability based design optimization, decision making in the face of uncertainty and testing for reliability certification. Applications in aerospace, automotive, civil and ocean engineering are presented. Success stories demonstrating the benefits of non deterministic approaches are included. A unique feature of the book is that it presents the perspectives of leaders from government labs, the industry and the academia on non deterministic methods. A pdf flier is attached to the mention of this book in the Books part of the interval computations website http://www.cs.utep.edu/interval-comp From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Jan 14 14:02:18 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0EK2IVB018994 for ; Fri, 14 Jan 2005 14:02:18 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0EK2HA5018993 for reliable_computing-outgoing; Fri, 14 Jan 2005 14:02:17 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0EK29Q8018989 for ; Fri, 14 Jan 2005 14:02:15 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j0EK21u28842 for ; Fri, 14 Jan 2005 13:02:01 -0700 (MST) Message-Id: <200501142002.j0EK21u28842 [at] cs [dot] utep.edu> Date: Fri, 14 Jan 2005 13:02:02 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: FYI To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: SSdThHJXKCLwYetK+1DJ8Q== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Status: O X-Status: $$$$ X-UID: 0000000036 Europe Fights Tide of Absurd Patents" New Scientist (01/08/05) Vol. 185, No. 2481, P. 22; Fox, Barry The European Parliament is likely to soon pass a European Commission directive that bans software and business method patents in order to avoid a patent inundation that could hamper technological innovation by encouraging infringement lawsuits. There is a long-standing consensus between European politicians and programmers that copyright already provides adequate protection for software, making broadly applicable software patents unwanted. But patent applicants have been exploiting a loophole that allows software to be patented as a computer-implemented invention--a loophole that the draft directive seeks to remove. The directive has traveled a bumpy road to approval by the parliament: The original draft did not clearly distinguish between software-controlled inventions and the software that controls such inventions, so a provision that banned pure software patents was inserted. However, the European Industry Association for Information Systems, Communication Technologies, and Consumer Electronics (EICTA) complained that the legislation's wording permitted a patented technique with a "significant purpose" to be used without infringement, so the commission and the parliament are debating a new draft that is expected to make allowances for computer-implemented inventions that include a "technical contribution." The Foundation for a Free Information Infrastructure's Rufus Pollock warns that such a term is vulnerable to overly broad interpretation that could permit software patenting. From: http://www.acm.org/technews/articles/2005-7/0114f.html#item17 From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Jan 15 13:37:51 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0FJbo1D021452 for ; Sat, 15 Jan 2005 13:37:50 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0FJboIE021451 for reliable_computing-outgoing; Sat, 15 Jan 2005 13:37:50 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0FJbm4w021447 for ; Sat, 15 Jan 2005 13:37:48 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0FJblpg021446 for reliable_computing [at] interval [dot] louisiana.edu; Sat, 15 Jan 2005 13:37:47 -0600 (CST) Received: from marnier.ucs.louisiana.edu (root [at] marnier [dot] ucs.louisiana.edu [130.70.132.233]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0FJbA6L021433 for ; Sat, 15 Jan 2005 13:37:15 -0600 (CST) Received: from goedel.louisiana.edu (root [at] goedel [dot] louisiana.edu [130.70.132.143]) by marnier.ucs.louisiana.edu (8.13.1/8.13.1/ull-ucs-mx-host_1.9) with ESMTP id j0FJb4S2006821 for ; Sat, 15 Jan 2005 13:37:09 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@interval [130.70.132.145]) by goedel.louisiana.edu (8.13.1/8.13.1/ull-standalone_2.5) with SMTP id j0FJaxQK017569 for ; Sat, 15 Jan 2005 13:37:04 -0600 (CST) Message-Id: <200501151937.j0FJaxQK017569 [at] goedel [dot] louisiana.edu> Date: Sat, 15 Jan 2005 13:37:04 -0600 (CST) From: "Kearfott R. Baker" Reply-To: "Kearfott R. Baker" Subject: re: polynomial variability To: reliable_computing [at] interval [dot] louisiana.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: od+JcQxmwTmK39gaF86U8w== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4.8 SunOS 5.8 sun4m sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Patrizia, Yes, that seems to be an interesting conjecture. Do I understand that you are conjecturing that, if you take the Taylor representation for a polynomial, the intervals of minimum width in the Taylor representation correspond to intervals of minimum width of the exact range? I don't know of results like that, although Martin Berz or his students may. You might also clarify the conjecture by reminding us how you are choosing the base point x_0, or if it matters. Someone should be able to come up with a proof or counterexample. Sincerely, Baker >From: "Patrizia Lamberti" >To: >Subject: re: polynomial variability >Date: Thu, 13 Jan 2005 17:00:31 +0100 >MIME-Version: 1.0 >X-Priority: 3 >X-MSMail-Priority: Normal >X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 >X-Spam-Score: (-1.424) BAYES_01,HTML_MESSAGE >X-Scanned-By: MIMEDefang 2.42 > >Dear prof. Kearfott, Demmel and Jiawang Nie, > >thank you very much for your prompt reply. > >I am afraid I was not very clear in the description of the problem. >Indeed, my objective is NOT the accurate evaluation of the exact range of the polynomial. Instead I am looking for an approach that gives me information about where the region of minimum variability of the function is located. To this aim, it is enough for me that the overestimation of the united extension is the minimum in the interval wherein the function shows the lowest sensitivity. Note that it is enough to know that we have THERE the minimum overestimation with respect to the overestimation obtained for the interval of the same width, but centered in any other point. > >Note that the range I look for may not to be coincident with a minimum/maximum of the function f(x). If the amplitude of the united extension f(X(k)) is w(f(X(k)))=max(f(X(k)))-min(f(X(k))), we are looking for the X(k) to which corresponds the minimum w(f(X(k))). That is the region of minimum variability. > >Now, I was trying an interval extension F(X(k)) of f(x) on the interval X(k) such that w(F(X(k))) had the same behaviour of w(f(X(k))). In particular that w(F(X(k))) was minimum just where w(f(X(k))) was, even if w(F(X(k)))>> w(f(X(k))). > >Actually, using the Taylor Model of f as interval extension (F_TM(X(k))), i.e. by using the complete Taylor series of f(x) around x0(k) and estimating it in terms of interval variable, I have verified that w(F(X(k))) keeps the presence of local and absolute minima just where local and absolute minima of w(f(X(k))) are. In particular it is true for a generic parabola and for all the polynomials that I have randomly obtained (from 3rd to 9th order). Moreover this characteristic is maintained for all delta, i.e. both tight and wide interval. > >I think improbable that these are only coincidences, rather I'm looking for a justification to this behaviour in the properties of the Taylor Model. >Can you help me about this topics? May this result be extended to any polynomial function? Are there some theorems about this? > >I have not found a precise reference to this topic in literature, but I am afraid I am not searching for in the right way. I am sure that you can address me in the right way. > >At the best of your knowledge, is somewhere anyone who has been interested in the region of minimum w(f(X(k))) rather than the minimum of f(X(k)), or the best inclusion of the function? > >Do you think that the use of TM is valid or suggest alternatives to me? > >Thanks in advance > >Patrizia Lamberti --------------------------------------------------------------- R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax) (337) 482-5270 (work) (337) 993-1827 (home) URL: http://interval.louisiana.edu/kearfott.html Department of Mathematics, University of Louisiana at Lafayette Box 4-1010, Lafayette, LA 70504-1010, USA --------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Jan 18 06:35:34 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0ICZX2Y027147 for ; Tue, 18 Jan 2005 06:35:33 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0ICZXdQ027146 for reliable_computing-outgoing; Tue, 18 Jan 2005 06:35:33 -0600 (CST) Received: from sophia.inria.fr (sophia.inria.fr [138.96.64.20]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0ICZNhj027142 for ; Tue, 18 Jan 2005 06:35:29 -0600 (CST) Received: from localhost (localhost [127.0.0.1]) by sophia.inria.fr (8.12.10/8.12.9) with ESMTP id j0ICZITB014043 for ; Tue, 18 Jan 2005 13:35:18 +0100 Received: from caphorn.inria.fr (caphorn.inria.fr [138.96.116.27]) by sophia.inria.fr (8.12.10/8.12.9) with ESMTP id j0ICY0Fp013470 for ; Tue, 18 Jan 2005 13:34:01 +0100 Received: (from merlet@localhost) by caphorn.inria.fr (8.12.10/8.12.5) id j0ICY0mB005400 for reliable_computing [at] interval [dot] louisiana.edu; Tue, 18 Jan 2005 13:34:00 +0100 (MET) Date: Tue, 18 Jan 2005 13:34:00 +0100 (MET) From: Jean-Pierre Merlet Message-Id: <200501181234.j0ICY0mB005400 [at] caphorn [dot] inria.fr> To: reliable_computing [at] interval [dot] louisiana.edu Subject: Copy of Ratscheck paper X-Greylist: Sender IP whitelisted, not delayed by milter-greylist-1.4 (sophia.inria.fr [138.96.64.20]); Tue, 18 Jan 2005 13:34:01 +0100 (MET) X-Virus-Scanned: by amavisd-new at sophia.inria.fr Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Hello, I am looking for an electronic copy of: Ratschek, H. and J. Rokne (1995). Formulas for the width of interval products. Reliable Computing 1, 9-14. Best J-P. Merlet From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Jan 18 08:30:51 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0IEUpR4027412 for ; Tue, 18 Jan 2005 08:30:51 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0IEUoDZ027411 for reliable_computing-outgoing; Tue, 18 Jan 2005 08:30:50 -0600 (CST) Received: from imap.univie.ac.at (mail.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0IEUeOq027407 for ; Tue, 18 Jan 2005 08:30:47 -0600 (CST) Received: from [131.130.16.23] (theseus.mat.univie.ac.at [131.130.16.23]) by imap.univie.ac.at (8.12.10/8.12.10) with ESMTP id j0IEURXK307276; Tue, 18 Jan 2005 15:30:29 +0100 Message-ID: <41ED1D7A.4060802 [at] univie [dot] ac.at> Date: Tue, 18 Jan 2005 15:30:18 +0100 From: Arnold Neumaier Organization: University of Vienna User-Agent: Mozilla Thunderbird 0.9 (X11/20041127) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Jean-Pierre Merlet CC: reliable_computing [at] interval [dot] louisiana.edu Subject: Re: Copy of Ratscheck paper References: <200501181234.j0ICY0mB005400 [at] caphorn [dot] inria.fr> In-Reply-To: <200501181234.j0ICY0mB005400 [at] caphorn [dot] inria.fr> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-DCC-ZID-Univie-Metrics: mx7.univie.ac.at 4249; Body=3 Fuz1=3 Fuz2=3 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Jean-Pierre Merlet wrote: > Hello, > > I am looking for an electronic copy of: > Ratschek, H. and J. Rokne (1995). Formulas for the width > of interval products. Reliable Computing 1, 9-14. Optimal formulas for midpoint and radius of the product are in Proposition 1.6.5 of my book A. Neumaier Interval Methods for Systems of Equations Cambridge Univ. Press, Cambridge 1990 I don't know how close they are to those by R/R. Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Jan 19 09:59:25 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0JFxPNW029524 for ; Wed, 19 Jan 2005 09:59:25 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0JFxPgU029523 for reliable_computing-outgoing; Wed, 19 Jan 2005 09:59:25 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0JFxGdD029519 for ; Wed, 19 Jan 2005 09:59:21 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j0JFxAA27859; Wed, 19 Jan 2005 08:59:11 -0700 (MST) Message-Id: <200501191559.j0JFxAA27859 [at] cs [dot] utep.edu> Date: Wed, 19 Jan 2005 08:59:10 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: 2nd CfP: ISIPTA'05 To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu Cc: fgcozman [at] usp [dot] br MIME-Version: 1.0 Content-Type: TEXT/plain; charset=ISO-8859-1 Content-MD5: B3L/iFlEAkLHUbENf4jhqg== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from QUOTED-PRINTABLE to 8bit by interval.louisiana.edu id j0JFxMdD029520 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk ------------- Begin Forwarded Message ------------- X-Authentication-Warning: swan2.uspnet.usp.br: fgcozman owned process doing -bs Date: Tue, 18 Jan 2005 16:21:55 -0200 (BRDT) From: Fabio Gagliardi Cozman Your help with circulating this announcement is much appreciated; note new submission deadline. Apologies for multiple postings. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ISIPTA '05 4th International Symposium on Imprecise Probabilities and Their Applications Second Call for Papers July 20-23, 2005 Carnegie Mellon University Pittsburgh, Pennsylvania, USA http://www.sipta.org/isipta05 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ The ISIPTA meetings are one of the primary international forums to present and discuss new results on the theory and applications of imprecise probabilities. Imprecise probability has a wide scope, being a generic term for the many mathematical or statistical models which measure chance or uncertainty without sharp numerical probabilities. These models include belief functions, Choquet capacities, comparative probability orderings, convex sets of probability measures, fuzzy measures, interval-valued probabilities, possibility measures, plausibility measures, and upper and lower expectations or previsions. Imprecise probability models are needed in inference problems where the relevant information is scarce, vague or conflicting, and in decision problems where preferences may also be incomplete. Themes of the symposium ----------------------- Although the symposium will be open to contributions on all aspects of imprecise probability, three main themes will be emphasised: decision-making, algorithms, and real applications. Topics of interest include, but are not limited to: models of coherent imprecise assessments convex sets of probability measures (credal sets) interval-valued probabilities upper and lower expectations or previsions non-additive set functions, and in particular Choquet capacities (and Choquet integration), fuzzy measures, possibility measures, belief and plausibility measures random sets rough sets comparative probability orderings qualitative reasoning about uncertainty imprecision in utilities and expected utilities limit laws for imprecise probabilities physical models of imprecise probability philosophical foundations for imprecise probabilities psychological models for imprecision and indeterminacy in probability assessments elicitation techniques for imprecise probabilities robust statistics probabilistic bounding analysis data mining with imprecise probabilities/missing data estimation and learning of imprecise probability models decision making with imprecise probabilities ambiguity aversion and economic models of imprecise probability uncertainty in financial markets algorithms for manipulating imprecise probabilities Dempster-Shafer theory information algebras and probabilistic argumentation systems probabilistic logic, propositional and first-order credal networks and other graphical models credal classification applications in statistics, economics, finance, management, engineering, computer science and artificial intelligence, psychology, philosophy and related fields Workshop on Financial Risk Assessment ------------------------------------- There will be a workshop addendum to the conference, to be held on July 24, with invited speakers on the topic of financial risk assessment, to which all of the ISIPTA'05 participants are welcome, at no additional registration cost. Details will be announced later. Location -------- ISIPTA '05 will be held at Carnegie Mellon University, in Pittsburgh, Pennsylvania, United States. Important dates --------------- (Note that we have moved the deadlines, as we moved dates a bit with the publisher!!) Paper submission deadline: February 25 2005 Notification of acceptance: April 15 2005 Deadline for revised papers: May 15 2005 Symposium: July 20-23 2005 Submissions and Proceedings --------------------------- We will accept papers only as PDF files with a limit of 8 pages in two-column format. Guidelines are available both in a PDF file and in a word file at the site http://www.sipta.org/isipta05/submit.html. The simplest way to produce an article that satisfies these requirements is to use Latex with the isipta2005.sty style, using guidelinesat the file isipta05.tex (or using this file as a template). Otherwise, use the file isipta2005.doc as template. Submission is electronic. You should introduce paper data and attach the PDF file by using the submission page. The Program Committee will decide which of the submitted papers are accepted, by carefully evaluating their originality, significance, technical soundness, and clarity of exposition. All the accepted papers will be included in a volume of proceedings, published by Brightdocs. There will be free electronic access to the proceedings after some time. Before the conference, the electronic access will be restricted to the ISIPTA '05 attendees to allow them to study the papers in some detail before they are actually presented. Each accepted paper will be given the opportunity for both a brief oral presentation as well as a poster session. Program Board ------------- Fabio Cozman (Universidade de Sao Paulo, Brazil) Robert Nau (Duke University, USA) Teddy Seidenfeld (Carnegie Mellon University, USA) Steering Committee ------------------ Gert de Cooman (Universiteit Gent, Belgium) Fabio G. Cozman (Universidade de São Paulo, Brazil) Serafin Moral (Universidad de Granada, Spain) Robert Nau (Duke University, USA) Teddy Seidenfeld (Carnegie Mellon University, USA) Marco Zaffalon (IDSIA-Istituto Dalle Molle di Studi sull'Intelligenza Artificiale, Switzerland) The members of the program committee are listed in the site www.sipta.org/isipta05.html. Questions --------- If you have any questions about the symposium, please contact the Organising Committee preferably by email (teddy [at] stat [dot] cmu.edu - fgcozman [at] usp [dot] br), or at the following address: Teddy Seidenfeld Department of Statistics Carnegie Mellon University Pittsburgh PA 15213 Phone: 412 - 268 - 2209 Fax: 412 - 268 - 1440 ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Jan 20 17:51:28 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0KNpS7Y002166 for ; Thu, 20 Jan 2005 17:51:28 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0KNpSja002165 for reliable_computing-outgoing; Thu, 20 Jan 2005 17:51:28 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0KNpJgc002160 for ; Thu, 20 Jan 2005 17:51:25 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j0KNotA08476; Thu, 20 Jan 2005 16:50:55 -0700 (MST) Message-Id: <200501202350.j0KNotA08476 [at] cs [dot] utep.edu> Date: Thu, 20 Jan 2005 16:50:54 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: a new book of potential interest to the interval computations community To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu Cc: meer [at] imada [dot] sdu.dk MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: OGcte0PW4BcPiDCMtUSGkA== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Hubertus Th. Jongen, Klaus Meer and Eberhard Triesch, "Optimization Theory", Kluwer Academic Publishers, Boston, Hardbound, ISBN 1-4020-8098-0, June 2004, For more details, including Table of Contents, see the book's webpage http://www.imada.sdu.dk/Research/OptimizationTheory/ (in particular, it has a lot of optimization complexity results, explained from scratch). Book's description: Optimization Theory is becoming a more and more important mathematical as well as interdisciplinary area, especially in the interplay between mathematics and many other sciences like computer science, physics, engineering, operations research, etc. This volume gives a comprehensive introduction into the theory of (deterministic) optimization on an advanced undergraduate and graduate level. One main feature is the treatment of both continuous and discrete optimization at the same place. This allows to study the problems under different points of view, supporting a better understanding of the entire field. Audience: The book can be adapted well as an introductory textbook into optimization theory on a basis of a two semester course; however, each of its parts can also be taught separately. Many exercises are included to increase the reader's understanding. From owner-reliable_computing [at] interval [dot] louisiana.edu Sun Jan 23 13:25:25 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0NJPP5S008043 for ; Sun, 23 Jan 2005 13:25:25 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0NJPPuK008042 for reliable_computing-outgoing; Sun, 23 Jan 2005 13:25:25 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0NJPGx7008038 for ; Sun, 23 Jan 2005 13:25:21 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j0NJP0e05077; Sun, 23 Jan 2005 12:25:02 -0700 (MST) Message-Id: <200501231925.j0NJP0e05077 [at] cs [dot] utep.edu> Date: Sun, 23 Jan 2005 12:25:00 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: scholarships at berlin To: reliable_computing [at] interval [dot] louisiana.edu Cc: griewank [at] mathematik [dot] hu-berlin.de MIME-Version: 1.0 Content-Type: TEXT/plain; charset=ISO-8859-1 Content-MD5: CHaZWVaqwwcdqVbYvFiWjQ== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from QUOTED-PRINTABLE to 8bit by interval.louisiana.edu id j0NJPMx7008039 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk apologies for multiple posting Dear Andreas, I hope you do not mind forwarding your email to the interval mailing list. Vladik ------------- Begin Forwarded Message ------------- Date: Sun, 23 Jan 2005 19:33:13 +0100 (CET) From: Andreas Griewank Dear Colleagues and/or Friends, As some of you may know I have moved to the Humboldt University Berlin, where I hold a professorship on nonlinear optimization attached to the DFG Reserach Center now named 'Matheon' Together with Carsten Carstensen, Barbara Niethammer and some other colleagues from Matheon we have established a 'Graduiertenkolleg', which is a temoporary graduate school. It provides this year 6 doctoral scholarships for master level applicants and 6 qualifying scholarships for bachelors. The focus of the study and research program is Analysis, Numerics, and Optimization of Multiphase Problems and we are looking for applicants from mathematics, physics and engineering with a keen interest and strong background in applied mathematics. While for the time being I am the coordinator, optimization is just one aspect and automatic differentiation won't figure prominently at all. I hope to learn a fair bit about PDEs myself. For some more details see http://multiphase.mathematik.hu-berlin.de Please encourage suitable students to contact us by e-mail and send in a resume. Preferably by the end of January, but there will probably be continuous admission throughout the first year depending on the quality of applicants. Also next year we'll get another batch of 6 scholarships and then later hopefully an extension for a second period of 4.5 years, so that a total of some 36 doctoral scholarships can be granted. The extra qualifying scholarships will only be available in the first year. We hope to attract significant foreign participation and everything will be conducted in English. With best wishes and the hope that this year will be more peaceful than the last, which unfortunately would not take much. Andreas Griewank fon: 49-30-2093 5820 sec: 49-30-2093 5833 ( Jutta Kerger ) fax: 49-30-2093 5859 mob: 49-178-6852592 url: math.hu-berlin.de/~griewank Institut für Mathematik Fakultät Mat.-Nat. II Humboldt-Universität Rudower Chaussee 25, Adlershof Post: Unter den Linden 6, 10099 Berlin Member of the DFG Research Center Matheon, Mathematics for Key Technologies home: Rosestr. 3a 12524 Berlin +4930 61504344 ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Sun Jan 23 20:01:48 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0O21mWm008554 for ; Sun, 23 Jan 2005 20:01:48 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0O21m6e008553 for reliable_computing-outgoing; Sun, 23 Jan 2005 20:01:48 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0O21dC8008549 for ; Sun, 23 Jan 2005 20:01:45 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j0O21ZU08246; Sun, 23 Jan 2005 19:01:35 -0700 (MST) Message-Id: <200501240201.j0O21ZU08246 [at] cs [dot] utep.edu> Date: Sun, 23 Jan 2005 19:01:34 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: possible interval session at IPMU'06 To: reliable_computing [at] interval [dot] louisiana.edu Cc: hunguyen [at] nmsu [dot] edu, Bernadette.Bouchon-Meunier [at] lip6 [dot] fr MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: F1wQmQBuQE2E6Ki8ZdXmOw== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Friends, Brenadette Bouchon-Meunier, the main organizer of the conference, will be very glad to have an interval session. She is a big interval enthusiast, e.g., she the editor-in-chief of the International Journal on Uncertainty, Fuzziness, and Knowledge-Based Systems (IJUFKS) that regularly publishes abstracts of interval application papers and had seevral interval-related special issues. If you are interested in participating in this session, please inform me and Hung T. Nguyen at vladik [at] cs [dot] utep.edu and hunguyen [at] nmsu [dot] edu The deadline is in October, so there is still time to decide. Your sincerely Vladik ********************************************** Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU'2006 July 2-7, 2006, Paris, France 1986-2006 Twenty Years of IPMU http://ipmu2006.lip6.fr Honorary President Lofti A. Zadeh General Chairpersons Bernadette Bouchon-Meunier Ronald R. Yager Topics Evidence Theory, Possibility Theory, Utility Theory, Measurement Theory, Belief Networks, Chaos Theory, Fuzzy Methods, Rough Sets, Belief Updating, Default Reasoning, Multivalued Logics, Temporal Reasoning, Machine Learning, Inductive Methods, Neural Networks, Aggregation Methods, Data Analysis, Fuzzy Control, Hybrid Systems, Clustering, Classification, Databases, Pattern Recognition, Image Processing, Bioinformatics, Information Incompleteness and Inconsistency, Multicriteria and Group Decision Making, Measure of Information and Uncertainty, Cyber Security Software Engineering, Bayesian and Probabilistic Methods, Diagnosis Expert Systems, Multi-Media Management, Decision Support Systems, Approximate Reasoning, Knowledge Acquisition, Knowledge Representation, Uncertainty in Cognition, Non-standard Logics, Non-monotonic Logics, Genetic Algorithms, Evolutionary Computation, Intelligent Systems, Medical Applications, Financial Engineering, Information Systems, Information Retrieval, Information Fusion, Data Mining Key Dates October 15, 2005 Submission of special sessions December 10, 2005 Submission of papers February 25, 2006 Notification of acceptance March 31, 2006 Submission of final papers July 2-7, 2006 Conference 3 copies of full paper (6-8 pages) must be submitted to the secretariat: Secretariat IPMU 2006 LIP6-Pole IA 8 rue du Capitaine Scott 75015 Paris, France ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Jan 24 10:52:43 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0OGqh1q010282 for ; Mon, 24 Jan 2005 10:52:43 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0OGqhML010281 for reliable_computing-outgoing; Mon, 24 Jan 2005 10:52:43 -0600 (CST) Received: from oceanite.ens-lyon.fr (oceanite.ens-lyon.fr [140.77.1.22]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0OGqX2s010277 for ; Mon, 24 Jan 2005 10:52:40 -0600 (CST) Received: from localhost (oceanite.ens-lyon.fr [127.0.0.1]) by oceanite.ens-lyon.fr (Postfix) with ESMTP id 8930D320814; Mon, 24 Jan 2005 17:42:39 +0100 (CET) Received: from oceanite.ens-lyon.fr ([127.0.0.1]) by localhost (oceanite [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id 19595-03; Mon, 24 Jan 2005 17:42:39 +0100 (CET) Received: from rakia.ens-lyon.fr (rakia.ens-lyon.fr [140.77.14.146]) by oceanite.ens-lyon.fr (Postfix) with ESMTP id 6232E320293; Mon, 24 Jan 2005 17:42:39 +0100 (CET) Date: Mon, 24 Jan 2005 17:49:32 +0100 (CET) From: Nathalie Revol X-X-Sender: nrevol [at] rakia [dot] ens-lyon.fr To: reliable_computing [at] interval [dot] louisiana.edu Cc: Gilles Villard , Nathalie Revol Subject: Postdoctoral Position at Ecole Normale Superieure, Lyon, France Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Virus-Scanned: by amavisd-new-20030616-p10 (Debian) at ens-lyon.fr Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Please distribute -- We apologize if you receive multiple copies of this announcement. POSTDOC POSITION IN COMPUTER SCIENCE ECOLE NORMALE SUPERIEURE, LYON FRANCE SOFTWARE COMPONENTS FOR VALIDATED SCIENTIFIC COMPUTING Other postdoc offers (cryptology, interval arithmetic) are available and can be consulted at http:// www.ens-lyon.fr/LIP/Arenaire/ Projet Arenaire / Laboratoire LIP (CNRS - ENSL - INRIA - UCBL) Ecole Normale Superieure 46 Allee d'Italie 69364 Lyon Cedex 07 France SUPERVISORS: Nathalie Revol (LIP-INRIA) (Nathalie.Revol@ens-lyon.fr), Gilles Villard (LIP-CNRS) (Gilles.Villard@ens-lyon.fr). RESEARCH PROJECT The candidate will be hosted by the Arenaire team of the LIP Laboratory. The goal is to contribute to the Roxane collaborative project: Reliable Open Software-Components for Algebraic and Numeric Efficiency (cf. Bernard.Mourrain [at] inria [dot] fr --- http://www-sop.inria.fr/galaad/logiciels/roxane). Roxane mutualizes and organizes the efforts of implementation that are done in different research groups in: computer arithmetic, computer algebra and numerical computing. In this context, the domain of expertise of Arnaire covers - arbitrary precision interval arithmetic and dedicated numerical algorithms, which lead to certified numerical results while still using floating-point arithmetic; - exact arithmetic especially for finite fields, rational numbers or polynomials. The candidate will work on these topics, including both algorithm design and software realizations. The algorithm side may concern linear algebra, lattice basis reduction, numerical constraint programming or optimization. Software aspects will include developments on Roxane, as well as works based on existing components, and the extension of their interoperability. SKILLS Candidates should have skills in computer arithmetic, and in one of the algorithmic domains mentioned in the research project. The programming language will be C or C++. PREFERRED DURATION: One year. TO APPLY: please contact ASAP Nathalie Revol (Nathalie.Revol@ens-lyon.fr) and Gilles Villard (Gilles.Villard@ens-lyon.fr). --------------------------------------------------------------------------- Nathalie REVOL INRIA Rhone Alpes LIP - Projet Arenaire tel : (33) 4-72-72-85-00 Ecole Normale Superieure de Lyon Fax : (33) 4-72-72-80-80 69364 Lyon Cedex 07, FRANCE Nathalie.Revol@ens-lyon.fr http://perso.ens-lyon.fr/nathalie.revol/ --------------------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Jan 24 13:13:24 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0OJDNlI010547 for ; Mon, 24 Jan 2005 13:13:23 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0OJDM7i010546 for reliable_computing-outgoing; Mon, 24 Jan 2005 13:13:22 -0600 (CST) Received: from mta10-winn.mailhost.ntl.com (smtpout18.mailhost.ntl.com [212.250.162.18]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0OJD7YY010542 for ; Mon, 24 Jan 2005 13:13:14 -0600 (CST) Received: from aamta01-winn.mailhost.ntl.com ([212.250.162.8]) by mta10-winn.mailhost.ntl.com with ESMTP id <20050124191259.PFDS20856.mta10-winn.mailhost.ntl.com@aamta01-winn.mailhost.ntl.com>; Mon, 24 Jan 2005 19:12:59 +0000 Received: from raynelubuwi4un ([81.109.113.141]) by aamta01-winn.mailhost.ntl.com with ESMTP id <20050124191207.JIKT15415.aamta01-winn.mailhost.ntl.com@raynelubuwi4un>; Mon, 24 Jan 2005 19:12:07 +0000 From: "H Huang" To: "'Nathalie Revol'" , Cc: "'Gilles Villard'" Subject: RE: Postdoctoral Position at Ecole Normale Superieure, Lyon, France Date: Mon, 24 Jan 2005 19:12:07 -0000 Message-ID: <000201c50248$9a8a6870$6401a8c0@raynelubuwi4un> MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="----=_NextPart_000_0003_01C50248.9A8A6870" X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook, Build 10.0.6626 Importance: Normal In-Reply-To: X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. ------=_NextPart_000_0003_01C50248.9A8A6870 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit Dear Nathalie and Gilles, I am writing to apply the postdoctoral position that is advertised on the mail list of reliable computing. I have neither pure computing background nor pure math background. But I have been engaged in mathematical modeling for many years and interested in interval arithmetic and reliable computing since 1998. In addition, I had half a year of French language training. I love French culture. I am sending you application materials for your consideration. I am a research fellow in the University of Leeds. My job is to develop computational method for model reduction for combustion process simulation. Before this job, I did my PhD study on quantitative process safety and flexibility analysis in the centre for process systems engineering of Imperial College London. I also had worked in process modeling and optimization for petroleum refining industry for years. I have strong intention to work on research of computational methodology for complex systems modeling, particularly for dynamic system (including systems biology) analysis and to apply those methods in different application areas. Having a multidisciplinary background, I am willing and prepared to collaborate with members of your department to fulfill ever changing research tasks. I have included my CV, publication and referee lists, research and teaching statements. Thank you for considering my application. I look forward to hearing from you and would be pleased to supply further information regarding my qualifications. Yours sincerely Haitao Huang Dr Haitao Huang 29 Raynel Drive Leeds LS16 6BS UK -----Original Message----- From: owner-reliable_computing [at] interval [dot] louisiana.edu [mailto:owner-reliable_computing [at] interval [dot] louisiana.edu] On Behalf Of Nathalie Revol Sent: 24 January 2005 16:50 To: reliable_computing [at] interval [dot] louisiana.edu Cc: Gilles Villard; Nathalie Revol Subject: Postdoctoral Position at Ecole Normale Superieure, Lyon, France Please distribute -- We apologize if you receive multiple copies of this announcement. POSTDOC POSITION IN COMPUTER SCIENCE ECOLE NORMALE SUPERIEURE, LYON FRANCE SOFTWARE COMPONENTS FOR VALIDATED SCIENTIFIC COMPUTING Other postdoc offers (cryptology, interval arithmetic) are available and can be consulted at http:// www.ens-lyon.fr/LIP/Arenaire/ Projet Arenaire / Laboratoire LIP (CNRS - ENSL - INRIA - UCBL) Ecole Normale Superieure 46 Allee d'Italie 69364 Lyon Cedex 07 France SUPERVISORS: Nathalie Revol (LIP-INRIA) (Nathalie.Revol@ens-lyon.fr), Gilles Villard (LIP-CNRS) (Gilles.Villard@ens-lyon.fr). RESEARCH PROJECT The candidate will be hosted by the Arenaire team of the LIP Laboratory. The goal is to contribute to the Roxane collaborative project: Reliable Open Software-Components for Algebraic and Numeric Efficiency (cf. Bernard.Mourrain [at] inria [dot] fr --- http://www-sop.inria.fr/galaad/logiciels/roxane). Roxane mutualizes and organizes the efforts of implementation that are done in different research groups in: computer arithmetic, computer algebra and numerical computing. In this context, the domain of expertise of Arnaire covers - arbitrary precision interval arithmetic and dedicated numerical algorithms, which lead to certified numerical results while still using floating-point arithmetic; - exact arithmetic especially for finite fields, rational numbers or polynomials. The candidate will work on these topics, including both algorithm design and software realizations. The algorithm side may concern linear algebra, lattice basis reduction, numerical constraint programming or optimization. Software aspects will include developments on Roxane, as well as works based on existing components, and the extension of their interoperability. SKILLS Candidates should have skills in computer arithmetic, and in one of the algorithmic domains mentioned in the research project. The programming language will be C or C++. PREFERRED DURATION: One year. TO APPLY: please contact ASAP Nathalie Revol (Nathalie.Revol@ens-lyon.fr) and Gilles Villard (Gilles.Villard@ens-lyon.fr). --------------------------------------------------------------------------- Nathalie REVOL INRIA Rhone Alpes LIP - Projet Arenaire tel : (33) 4-72-72-85-00 Ecole Normale Superieure de Lyon Fax : (33) 4-72-72-80-80 69364 Lyon Cedex 07, FRANCE Nathalie.Revol@ens-lyon.fr http://perso.ens-lyon.fr/nathalie.revol/ --------------------------------------------------------------------------- ------=_NextPart_000_0003_01C50248.9A8A6870 Content-Type: application/pdf; name="haitao_cvlb.pdf" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="haitao_cvlb.pdf" JVBERi0xLjMNJeLjz9MNCjUwIDAgb2JqDTw8IA0vTGluZWFyaXplZCAxIA0vTyA1MiANL0ggWyAx MTgwIDQyNiBdIA0vTCAyODUwNDYgDS9FIDEyMzI0MCANL04gMTEgDS9UIDI4MzkyOCANPj4gDWVu ZG9iag0gICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg 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(mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0RKFKuL017143 for ; Thu, 27 Jan 2005 14:15:26 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j0RKFBw07055; Thu, 27 Jan 2005 13:15:11 -0700 (MST) Message-Id: <200501272015.j0RKFBw07055 [at] cs [dot] utep.edu> Date: Thu, 27 Jan 2005 13:15:10 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Last Call - International Conference Virtual Concept 2005 To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu Cc: mceberio [at] utep [dot] edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: n8rwputz9dAUq3ymV9oeuw== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk ------------- Begin Forwarded Message ------------- From: j.corral [at] estia [dot] fr The 3rd International Conference Virtual Concept 2005 http://www.virtualconcept.estia.fr November 8 - 10th, 2005 Biarritz - FRANCE Dear colleagues, We remind you that deadlines for abstract submissions have been extended to the 4th of February 2005. Please notice that the online submission website will be closed at this date. You can submit a 200 words abstract on our website for: - an article: http://www.virtualconcept.estia.fr/call4paper.php?logout=1 - an invited session: http://www.virtualconcept.estia.fr/call4invited.php?logout=1 - a tutorial: http://www.virtualconcept.estia.fr/call4tutorial.php?logout=1 Looking forward to welcome you in Biarritz! On behalf of the Publicity and Scientific Committee Chairs of Virtual Concept 2005 ----------------------------------------------------------------------- The 3rd International Conference Virtual Concept 2005 http://www.virtualconcept.estia.fr November 8 - 10th, 2005 Biarritz - FRANCE Virtual Concept 2005 will bring together researchers and practitioners to discuss current advances, issues, and case studies in key technical areas of Virtual Reality dedicated to the product design, product manufacturing or industrial process implementation. This international conference will be held at Biarritz, in the south-west of France, between the Atlantic Ocean and Pyrenean mountains. Papers, invited sessions, tutorials from design, mechanical, computer science and industrial engineering fields may cover aspects of innovative theories and applications of Virtual Reality tools and techniques. Papers and invited session articles will be published within the proceedings of the conference edited by Springer Verlag. The chairmen of invited sessions will co-edit the proceedings of the conference. Best papers will be selected for publication in an international journal and also best communication and poster awards will be organized. ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Jan 28 04:29:04 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0SAT4eD018606 for ; Fri, 28 Jan 2005 04:29:04 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0SAT4D8018605 for reliable_computing-outgoing; Fri, 28 Jan 2005 04:29:04 -0600 (CST) Received: from imap.univie.ac.at (mail.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0SASswY018600 for ; Fri, 28 Jan 2005 04:29:00 -0600 (CST) Received: from [131.130.16.23] (theseus.mat.univie.ac.at [131.130.16.23]) by imap.univie.ac.at (8.12.10/8.12.10) with ESMTP id j0SASgR0334662; Fri, 28 Jan 2005 11:28:47 +0100 Message-ID: <41FA13B8.6090304 [at] univie [dot] ac.at> Date: Fri, 28 Jan 2005 11:28:08 +0100 From: Arnold Neumaier Organization: University of Vienna User-Agent: Mozilla Thunderbird 0.9 (X11/20041127) X-Accept-Language: en-us, en MIME-Version: 1.0 To: interval Subject: [Fwd: Postdoctoral position in Nantes, France] Content-Type: multipart/mixed; boundary="------------020908030407000103050602" X-DCC-ZID-Univie-Metrics: mx8 4248; Body=2 Fuz1=2 Fuz2=2 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. --------------020908030407000103050602 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit --------------020908030407000103050602 Content-Type: message/rfc822; name="Postdoctoral position in Nantes, France" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Postdoctoral position in Nantes, France" Path: usenet.univie.ac.at!aconews-feed.univie.ac.at!137.208.8.79.MISMATCH!bird.wu-wien.ac.at!newsfeed.wu-wien.ac.at!newsfeed.utanet.at!news.glorb.com!postnews.google.com!not-for-mail From: christophe.jermann [at] laposte [dot] net (Christophe Jermann) Newsgroups: sci.op-research,sci.research.postdoc Subject: Postdoctoral position in Nantes, France Date: 28 Jan 2005 01:15:49 -0800 Organization: http://groups.google.com Message-ID: <841cbd37.0501280115.232c43cf [at] posting [dot] google.com> NNTP-Posting-Host: 82.224.250.165 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1106903749 14481 127.0.0.1 (28 Jan 2005 09:15:49 GMT) X-Complaints-To: groups-abuse [at] google [dot] com NNTP-Posting-Date: Fri, 28 Jan 2005 09:15:49 +0000 (UTC) Xref: usenet.univie.ac.at sci.research.postdoc:11637 sci.op-research:21563 [apologies if you receive multiple copies of this message] POSTDOCTORAL POSITION in COMPUTER SCIENCE and INTERVAL MATHEMATICS University of Nantes, LINA laboratory, CoCoA Team ----- The CoCoA (Continuous Constraints and Applications) team of the LINA (Computer Science Laboratory of Nantes Atlantique) laboratory invites applications for a postdoctoral position. The appointment will be for one year, starting between September 2005 and December 2005. The CoCoA team will support candidates into applying to fellowships and grants programs. For this purpose, interested candidates should send their application the sooner. Context ------- The CoCoA team consists of 15 researchers who aim at solving general first-order formulas over integers and reals, involving non-linear constraints, uncertainty, preferences on the data and efficiency criteria. The base tools we use are interval analysis, constraint propagation (CP), symbolic computation and tree-search methods. Constraint programming provides a declarative and natural way of formulating problems as constraint satisfaction problems (CSPs) by stating the requirements (constraints) that must be fulfilled by the solutions. The CoCoA team is especially interested in numerical CSPs which involve constraints over real numbers. Such CSPs appear in industrial applications like conceptual design, computer aided design, robotics and molecular biology, which are the main applications the CoCoA team is tackling. Objectives ---------- The postdoctoral fellow will be involved into one of the ongoing research projects of the team, contribute to the development of the ELISA platform for constraint programming and optimization, and pursue researches in one of the following directions (depending on her/his abilities and desires): * hybridization of solving/optimization techniques (local/global, numeric/symbolic, ...) * design of solving/optimization methods for composite problems (hierarchical conjunctive/disjunctive models, mixed problems) * definition of systems and languages for constraint programming and optimization * study of a given application field (design, bioinformatics, ...) Candidate profile ----------------- Interested candidates should send an application letter including detailed CV (with a list of publications and a description of research interests) to the contacts below. The candidate must hold a recent PhD (within 5 years) at the appointment time. Applicants must have sound publications and expertise in one or more of the following areas (in a broad sense): * Programming languages and constraint programming * Optimization techniques (interval, convex, local, global, ...) * Cooperative problem solving Environment ------------ The city of Nantes is ideally located, only two hours from Paris by TGV (high-speed train, 20 shuttles per day) and about two hours by plane from most European capitals. Gateway to the Brittany ports, just a step away from major tourist sites such as Mont Saint-Michel, the Puy du Fou, the Futuroscope or the "Chateaux de la Loire", Nantes is also only 50km away from the renown coasts of Brittany and beaches of Vendee. The LINA laboratory offers a friendly working environment and excellent computational facilities. Contacts -------- Laurent Granvilliers or Christophe Jermann Laboratoire LINA - University of Nantes 2 rue de la Houssiniere BP 92208 F-44322 Nantes CEDEX France Phone: +33 251 125 851 or +33 251 125 840 Fax: +33 251 125 812 email: {laurent.granvilliers, christophe.jermann}@univ-nantes.fr http://www.sciences.univ-nantes.fr/lina/en/research/teams/COCOA/index.html --------------020908030407000103050602-- From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Jan 28 13:12:48 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0SJCmAu019268 for ; Fri, 28 Jan 2005 13:12:48 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j0SJCmC0019267 for reliable_computing-outgoing; Fri, 28 Jan 2005 13:12:48 -0600 (CST) Received: from oceanite.ens-lyon.fr (oceanite.ens-lyon.fr [140.77.1.22]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0SJCc6K019263 for ; Fri, 28 Jan 2005 13:12:45 -0600 (CST) Received: from localhost (oceanite.ens-lyon.fr [127.0.0.1]) by oceanite.ens-lyon.fr (Postfix) with ESMTP id 751A8320712; Fri, 28 Jan 2005 20:01:02 +0100 (CET) Received: from oceanite.ens-lyon.fr ([127.0.0.1]) by localhost (oceanite [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id 27062-01; Fri, 28 Jan 2005 20:01:02 +0100 (CET) Received: from rakia.ens-lyon.fr (rakia.ens-lyon.fr [140.77.14.146]) by oceanite.ens-lyon.fr (Postfix) with ESMTP id 463DD3206F3; Fri, 28 Jan 2005 20:01:02 +0100 (CET) Date: Fri, 28 Jan 2005 20:07:56 +0100 (CET) From: Nathalie Revol X-X-Sender: nrevol [at] rakia [dot] ens-lyon.fr To: reliable_computing [at] interval [dot] louisiana.edu Cc: Nathalie Revol Subject: Postdoctoral position, Lyon, France Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Virus-Scanned: by amavisd-new-20030616-p10 (Debian) at ens-lyon.fr Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Please distribute -- We apologize if you receive multiple copies of this announcement. POSTDOC POSITION IN COMPUTER SCIENCE ECOLE NORMALE SUPERIEURE, LYON FRANCE IMPLEMENTATION OF A VALIDATED INFINITE NORM Other postdoc offers (cryptology, computer algebra) are available and can be consulted at http:// www.ens-lyon.fr/LIP/Arenaire/ KEYWORDS: infinite norm, elementary functions, interval arithmetic, variable precision SUPERVISORS: Jean-Michel Muller {Jean-Michel.Muller@ens-lyon.fr}, Nathalie Revol {Nathalie.Revol@ens-lyon.fr} LOCATION: LIP + address + url PREFERRED DURATION: 12 months ARENAIRE PROJECT Arenaire is a project of 16 researchers which aims at elaborating and consolidating knowledge in the field of computer arithmetic. We contribute to the improvement of the available arithmetic, at the hardware level as well as at the software level, on computers, processors, dedicated or embedded chips, etc. Reliability, accuracy, and speed are major goals that drive our studies. We also take into account other constraints such as power consumption, certification using formal proof techniques or reliability of numerical software. Target arithmetics are fixed or floating point format, interval arithmetic, finite fields arithmetic and multiple precision. SCIENTIFIC CONTEXT: One of the research topics of Arenaire is the hardware or software computation, as efficiently as possible, of elementary functions (sine, exponential, arc-tangent...). The notion of efficiency is related to the target application (computing time, memory, circuit area, accuracy). The method consists in approximating the considered elementary function f by a polynomial, on a fixed domain (usually a small interval) and thus the polynomial of given degree that best approximates f is sought; constraints may be added on the coefficients of the polynomial. For a candidate polynomial p, the quality of the approximation is measured by the infinite norme of the error (f-p) on the considered interval and our goal is to bound as accurately as possible this error and to get validated bounds. RESEARCH PROJECT: Given a function f (given analytically and not by its value at some points), a polynomial p and an interval I, the candidate will have to design and implement an algorithm that provides bounds (upper and lower bounds) of the infinite norm of (f-p) on I. - The result must be validated in order to guarantee the quality of the approximation: this will be obtained via interval arithmetic. - The computing precision is variable and not one of the usual (single or double) computing precision: indeed, intermediate computations of the error require more precision than the target precision; furthermore, some applications concern digital signal processing, where the precision differs from the usual ones. A possible extension concerns the determination of the best polynomial of given degree, when constraints on the coefficients are to be taken into account. EXISTING WORK: the library MPFI implements interval arithmetic with variable and arbitrary precision. Language: C/C++. SKILLS: PhD in computer science or numerical analysis - PhD in computer science + basic knowledge in NA - PhD in numerical analysis + programming, preferrably in C/C++ CONTACT: contact ASAP Jean-Michel Muller {Jean-Michel.Muller@ens-lyon.fr}, Nathalie Revol {Nathalie.Revol@ens-lyon.fr} --------------------------------------------------------------------------- Nathalie REVOL INRIA Rhone Alpes LIP - Projet Arenaire tel : (33) 4-72-72-85-00 Ecole Normale Superieure de Lyon Fax : (33) 4-72-72-80-80 69364 Lyon Cedex 07, FRANCE Nathalie.Revol@ens-lyon.fr http://perso.ens-lyon.fr/nathalie.revol/ ---------------------------------------------------------------------------