From owner-reliable_computing Wed Jun 4 05:04:28 1997 Received: by interval.usl.edu id AA11287 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Wed, 4 Jun 1997 12:40:35 -0500 Received: from cs.utep.edu by interval.usl.edu with SMTP id AA11281 (5.65c/IDA-1.4.4 for ); Wed, 4 Jun 1997 12:40:31 -0500 Received: from earth.cs.utep.edu by cs.utep.edu (4.1/SMI-4.1) id AA12186; Wed, 4 Jun 97 11:04:28 MDT Date: Wed, 4 Jun 97 11:04:28 MDT From: vladik [at] cs [dot] utep.edu (Vladik Kreinovich) Message-Id: <9706041704.AA12186 [at] cs [dot] utep.edu> To: reliable_computing [at] interval [dot] usl.edu Subject: source for programming languages Cc: sisasa [at] utu [dot] fi Sender: owner-reliable_computing Precedence: bulk Dear Friends. >From a CS Education mailing list, I have just learned about a comprehensive web site http://www.utu.fi:80/~sisasa/oasis/ that contains, among other things, lots of information and links to various programming languages. As of now, links to interval languages are missing. I have informed the maintainer of this list, Simo Salminen (email sisasa [at] utu [dot] fi) about the links to interval computations languages that he may borrow from the links at the Interval Computations website (http://cs.utep.ed/interval-comp/main.html, click on Languages). If there is any langauge and/or link missing in this site please inform me and him. Thanks. Vladik From owner-reliable_computing Thu Jun 5 05:52:46 1997 Received: by interval.usl.edu id AA11936 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Thu, 5 Jun 1997 10:50:24 -0500 Received: from STUIO2.puce.edu.ec by interval.usl.edu with SMTP id AA11930 (5.65c/IDA-1.4.4 for ); Thu, 5 Jun 1997 10:47:49 -0500 Received: by stuio2.puce.edu.ec with SMTP (Microsoft Exchange Server Internet Mail Connector Version 4.0.995.52) id <01BC719E.87D1DB20 [at] stuio2 [dot] puce.edu.ec>; Thu, 5 Jun 1997 10:52:15 -0500 Message-Id: From: CASARES ALEJANDRO To: =?iso-8859-1?Q?=27Alberto_Pazmi=F1o=27?= , 'AUSJAL' , 'Cleve Moler' , 'Computacion confiable' , "'Correo automatico de tgc.com'" , =?iso-8859-1?Q?=27Fundaci=F3n_Tele_Amigo=27?= To: 'HPC circulacion' , "'Java World, editor en jefe'" , 'NA teach' , =?iso-8859-1?Q?=27Nelson_Pe=F1arreta=27?= Subject: New email address Date: Thu, 5 Jun 1997 10:52:46 -0500 X-Mailer: Microsoft Exchange Server Internet Mail Connector Version 4.0.995.52 Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Sender: owner-reliable_computing Precedence: bulk Dear friends: Please, be aware of my "new" email address: It is: acasares [at] puceuio [dot] puce.edu.ec Greetings, Alejandro Casares Maldonado Pontificia Universidad Cat=F3lica del Ecuador Facultad de Ingenier=EDa QUITO, ECUADOR From owner-reliable_computing Wed Jun 11 04:12:13 1997 Received: by interval.usl.edu id AA13832 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Tue, 10 Jun 1997 03:12:36 -0500 Received: from ness.arch.usyd.EDU.AU (elvis.arch.usyd.EDU.AU) by interval.usl.edu with SMTP id AA13826 (5.65c/IDA-1.4.4 for ); Tue, 10 Jun 1997 03:12:31 -0500 Received: from katrine.arch.su.EDU.AU. (katrine [129.78.66.228]) by ness.arch.usyd.EDU.AU (8.7.5/8.7.3) with ESMTP id SAA18283 for ; Tue, 10 Jun 1997 18:12:15 +1000 (EST) Received: from mailclient (localhost [127.0.0.1]) by katrine.arch.su.EDU.AU. (8.7.5/8.7.3) with ESMTP id SAA03560 for ; Tue, 10 Jun 1997 18:12:14 +1000 (EST) Message-Id: <199706100812.SAA03560 [at] katrine [dot] arch.su.EDU.AU.> To: reliable_computing [at] interval [dot] usl.edu Subject: Interval extensions of Relational DBMS Date: Tue, 10 Jun 1997 18:12:13 +1000 From: Simeon Simoff Sender: owner-reliable_computing Precedence: bulk Here is a reference to an interesting work for those who try to use intervals in managing uncertainty in data- and knowledge-based systems. A Note on "Incomplete Relational Database Models Based on Intervals" Jui-Shang Chiu and Arbee L. P. Chen Abstract--In, a family of relational database models (M-1 to M-5) were proposed to represent unknown values by intervals. Relational operators were extended for evaluating queries on these models. In this note, we stultify the theorems claiming that query evaluation in models M-2, M-3, and M-5 is sound. Index Terms--Incomplete information, disjunctive information, null values, extended relational model, extended relational algebra. The authors are with the Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China. E-mail: alpchen [at] cs [dot] nthu.edu.tw. IEEE Transactions on Knowledge and Data Engineering, Vol. 8, No. 1, February 1996 Copyright (c) 1996 Institute of Electrical and Electronics Engineers, Inc. All rights reserved. From owner-reliable_computing Tue Jun 10 02:34:37 1997 Received: by interval.usl.edu id AA14256 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Tue, 10 Jun 1997 09:34:47 -0500 Received: from cs.utep.edu by interval.usl.edu with SMTP id AA14250 (5.65c/IDA-1.4.4 for ); Tue, 10 Jun 1997 09:34:44 -0500 Received: from earth.cs.utep.edu by cs.utep.edu (4.1/SMI-4.1) id AA06600; Tue, 10 Jun 97 08:34:37 MDT Date: Tue, 10 Jun 97 08:34:37 MDT From: vladik [at] cs [dot] utep.edu (Vladik Kreinovich) Message-Id: <9706101434.AA06600 [at] cs [dot] utep.edu> To: reliable_computing [at] interval [dot] usl.edu Subject: Re: Interval extensions of Relational DBMS Sender: owner-reliable_computing Precedence: bulk > Here is a reference to an interesting work for those who try to use intervals > in managing uncertainty in data- and knowledge-based systems. > > A Note on "Incomplete Relational Database Models Based on Intervals" > Jui-Shang Chiu and Arbee L. P. Chen Dear Colleagues, I want to use this opportunity: * to thank Dr. Simoff for a reference to a really interesting article, and * to (once again) ask the subscribers of this mailing list who deal with applications of interval to send me their abstracts and/or references to the two journal sections that cover these application: * a regular section in the "International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems" (IJUFKS) publishes abstracts of papers in which intervals are used in knowledge representation and uncertainty processing; * a regular section in "Reliable Computing" covers various other applications of interval computations and of other techniques of scientific reliable computing. In particular, a brief abstract of the article by Chiu is published, as part of the applications section, in IJUFKS, 1996, Vol. 4, No. 5, p. 470. Vladik From owner-reliable_computing Wed Jun 11 12:00:46 1997 Received: by interval.usl.edu id AA15412 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Wed, 11 Jun 1997 15:00:52 -0500 Received: from mail4.uts.ohio-state.edu by interval.usl.edu with SMTP id AA15406 (5.65c/IDA-1.4.4 for ); Wed, 11 Jun 1997 15:00:49 -0500 Received: from ts29-15.homenet.ohio-state.edu (ts29-15.homenet.ohio-state.edu [140.254.114.102]) by mail4.uts.ohio-state.edu (8.8.5/8.8.5) with SMTP id QAA17116 for ; Wed, 11 Jun 1997 16:00:46 -0400 (EDT) Date: Wed, 11 Jun 1997 16:00:46 -0400 (EDT) Message-Id: <199706112000.QAA17116 [at] mail4 [dot] uts.ohio-state.edu> X-Sender: rmoore [at] pop [dot] service.ohio-state.edu X-Mailer: Windows Eudora Pro Version 2.1.2 Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: reliable_computing [at] interval [dot] usl.edu From: Ramon Edgar Moore Subject: Mathematics Subject Classification Sender: owner-reliable_computing Precedence: bulk Dear Colleagues, On page 2 of the June 1997 SIAM NEWS is an article about providing input to a committee considering updates of the 1991 Mathematics Subject Classification for Mathematical Reviews and Zentralblatt fuer Mathematik. The existing classification scheme is found at http://www.ams.org/msc/ Suggestions may be sent to any or all of the committee members martinez [at] ime [dot] unicamp.br lex.schrijver [at] cwi [dot] nl miketodd [at] cs [dot] cornell.edu So far, interval mathematics appears only under numerical analysis, in the subheading under error analysis. Perhaps some suggestions are in order for additional listings. Ramon E. Moore From owner-reliable_computing Wed Jun 11 10:40:24 1997 Received: by interval.usl.edu id AA15684 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Wed, 11 Jun 1997 15:40:25 -0500 Received: from bp.ucs.usl.edu by interval.usl.edu with SMTP id AA15678 (5.65c/IDA-1.4.4 for ); Wed, 11 Jun 1997 15:40:23 -0500 Received: from rbk5287.usl.edu (liberty.usl.edu) (liberty.usl.edu [130.70.46.171]) by bp.ucs.usl.edu with SMTP id AA15730 (5.65c/IDA-1.4.4 for ); Wed, 11 Jun 1997 15:40:22 -0500 Message-Id: <2.2.32.19970611204024.00b35060 [at] pop [dot] usl.edu> X-Sender: rbk5287 [at] pop [dot] usl.edu X-Mailer: Windows Eudora Pro Version 2.2 (32) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Wed, 11 Jun 1997 15:40:24 -0500 To: reliable_computing [at] interval [dot] usl.edu From: "R. Baker Kearfott" Subject: Re: Mathematics Subject Classification Sender: owner-reliable_computing Precedence: bulk Ray, Vladik Kreinovich took the initiative a few months ago, and we discussed it at some length. As far as I know, vladik has made recommendations to the committee according to our discussions. However, I am sure there is still room for more input. I suggest that interested persons contact Vladik at vladik [at] cs [dot] utep.edu to obtain what we have already submitted, and then proceed further. On the other hand, hearing from many of us may also underline the importance of the subject :-) Best regards, Baker At 04:00 PM 6/11/97 -0400, Ramon Edgar Moore wrote: >Dear Colleagues, > >On page 2 of the June 1997 SIAM NEWS is an article about providing input to >a committee considering updates of the 1991 Mathematics Subject >Classification for Mathematical Reviews and Zentralblatt fuer Mathematik. > >The existing classification scheme is found at > > http://www.ams.org/msc/ > >Suggestions may be sent to any or all of the committee members > > martinez [at] ime [dot] unicamp.br > > lex.schrijver [at] cwi [dot] nl > > miketodd [at] cs [dot] cornell.edu > >So far, interval mathematics appears only under numerical analysis, in the >subheading under error analysis. Perhaps some suggestions are in order for >additional listings. > >Ramon E. Moore > > > --------------------------------------------------------------- R. Baker Kearfott, rbk [at] usl [dot] edu (318) 482-5346 (fax) (318) 482-5270 (work) (318) 981-9744 (home) URL: http://interval.usl.edu/kearfott.html Department of Mathematics, University of Southwestern Louisiana USL Box 4-1010, Lafayette, LA 70504-1010, USA --------------------------------------------------------------- From owner-reliable_computing Thu Jun 12 08:43:00 1997 Received: by interval.usl.edu id AA16631 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Thu, 12 Jun 1997 15:43:12 -0500 Received: from cs.utep.edu by interval.usl.edu with SMTP id AA16625 (5.65c/IDA-1.4.4 for ); Thu, 12 Jun 1997 15:43:08 -0500 Received: from earth.cs.utep.edu by cs.utep.edu (4.1/SMI-4.1) id AA04510; Thu, 12 Jun 97 14:43:00 MDT Date: Thu, 12 Jun 97 14:43:00 MDT From: vladik [at] cs [dot] utep.edu (Vladik Kreinovich) Message-Id: <9706122043.AA04510 [at] cs [dot] utep.edu> To: reliable_computing [at] interval [dot] usl.edu Subject: interval issue of IJUFKS Sender: owner-reliable_computing Precedence: bulk Dear Friends, I want to inform you that a special issue of the International Journal of Uncertainty, Fuzziness, and Knowledge-Based Reasoning (IJUFKS) devoted to interval methods in representing and processing uncertainty has just been published (its contents is attached). In addition to regular papers, this issue contains a special section with abstracts of recent papers on application of interval methods to knowledge representation. This section regularly appears in IJUFKS. Information about IJUFKS can be found at http://www.wspc.com.sg/journals/ijufks/ijufks.html June 1997 (Volume 5, Number 3) Guest Editors' Introduction: Interval Methods in Representing and Processing Uncertainty V. Kreinovich (page 221) A Mathematical Setting for Fuzzy Logics M. Gehrke, C. Walker, and E. Walker (page 223) Interval Methods and Fuzzy Optimization W. A. Lodwick and K. D. Jamison (page 239) >From Intervals to Fuzzy Truth-Values: Adding Flexibility to Reasoning Under Uncertainty R. L. de Mantaras and L. Godo (page 251) Reasoning with Uncertainty in Deductive Databases and Logic Programs R. T. Ng (page 261) Interval-Valued Degrees of Belief: Applications of Interval Computations to Expert Systems and Intelligent Control H. T. Nguyen, V. Kreinovich, and Q. Zuo (page 317) On Capacity Functionals in Interval Probabilities H. T. Nguyen, N. T. Nguyen, and T. Wang (page 359) Local Radon-Nikodym Derivatives of Set Functions J. Harding, M. Marinacci, N. T. Nguyen, and T. Wang (page 379) Interval Methods in Knowledge Representation (Abstracts of Recent Papers) V. Kreinovich (page 395) Calendar of Events (page 397) From owner-reliable_computing Fri Jun 13 04:01:36 1997 Received: by interval.usl.edu id AA17114 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Fri, 13 Jun 1997 07:01:43 -0500 Received: from mail2.uts.ohio-state.edu by interval.usl.edu with SMTP id AA17108 (5.65c/IDA-1.4.4 for ); Fri, 13 Jun 1997 07:01:39 -0500 Received: from ts15-9.homenet.ohio-state.edu (ts15-9.homenet.ohio-state.edu [140.254.113.64]) by mail2.uts.ohio-state.edu (8.8.5/8.8.5) with SMTP id IAA07391 for ; Fri, 13 Jun 1997 08:01:36 -0400 (EDT) Date: Fri, 13 Jun 1997 08:01:36 -0400 (EDT) Message-Id: <199706131201.IAA07391 [at] mail2 [dot] uts.ohio-state.edu> X-Sender: rmoore [at] pop [dot] service.ohio-state.edu X-Mailer: Windows Eudora Pro Version 2.1.2 Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: reliable_computing [at] interval [dot] usl.edu From: Ramon Edgar Moore Subject: re:Mathematics Subject Classification Sender: owner-reliable_computing Precedence: bulk FYI: >Date: Thu, 12 Jun 1997 09:26 -0400 (EDT) >From: Bill Older >Subject: re:Mathematics Subject Classification >Sender: Bill Older >To: moore.47 [at] osu [dot] edu > >Dr. Moore, > >I found your note concerning the classification of interval analysis >interesting. One can see it, I suppose, based on its early history, >but it seems rather peculiar now. The numeric connection in general-- >and the concentration on "errors" -- seem to me to be very incidental >features. > >But one could make a case for it to go to several places: as a >theoretical discipline it could be classfied under analysis I would >think, but a case for putting it under real topology or even >intuitionist logic could be possible. > >In the context in which I work I have always regarded interval >techniques as a particular kind of "applied lattice theory". > >Bill Older > > From owner-reliable_computing Sat Jun 14 10:39:00 1997 Received: by interval.usl.edu id AA18185 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Sat, 14 Jun 1997 15:39:08 -0500 Received: from boris.mscs.mu.edu by interval.usl.edu with SMTP id AA18179 (5.65c/IDA-1.4.4 for ); Sat, 14 Jun 1997 15:39:05 -0500 Received: by boris.mscs.mu.edu (Smail3.1.28.1 #9) id m0wczbA-0010tjC; Sat, 14 Jun 97 15:39 CDT Message-Id: From: georgec [at] marque [dot] mscs.mu.edu (Dr. George F. Corliss MU MSCS) Subject: Positions: Industrial-based GRAs at Marquette Univ. To: reliable_computing [at] interval [dot] usl.edu Date: Sat, 14 Jun 1997 15:39:00 -0500 (CDT) Cc: georgec [at] marque [dot] mscs.mu.edu (George Corliss) X-Mailer: ELM [version 2.4 PL25] Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Content-Length: 1418 Sender: owner-reliable_computing Precedence: bulk Industrial-Based Graduate Research Assistantships Department of Mathematics, Statistics, and Computer Science Marquette University, Milwaukee, Wisconsin, USA The Marquette University Department of Mathematics, Statistics, and Computer Science has openings for two Industrial-Based Graduate Research Assistantships in industrial and applied mathematics. Students will pursue a Master of Science degree while working closely with industrial sponsors Johnson Controls and Penta Technologies. One assistantship requires skills in operations research, the other in optimization and database design. Number of openings: two Start date: August 15, 1997 Annual stipend: $12,000 + tuition, jointly funded by NSF and industrial partners Students from groups traditionally underrepresented in the field are especially sought. The NSF funding requires students to be citizens of the USA or lawfully admitted permanent resident aliens. An on-site interview will normally be required. For information: To apply: Dr. George Corliss The Graduate School georgec [at] mscs [dot] mu.edu Marquette University 414 288-6599 PO Box 1881 Milwaukee, WI 53201-1881 414 288-7137 Fax: 414 288-1902 MUGS [at] vms [dot] csd.mu.edu For further information: Web: http://www.mscs.mu.edu/~georgec/Jobs/indust_gra.html From owner-reliable_computing Mon Jun 16 10:51:10 1997 Received: by interval.usl.edu id AA28980 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Wed, 18 Jun 1997 04:18:58 -0500 Received: from rztsun.rz.tu-harburg.de by interval.usl.edu with SMTP id AA28974 (5.65c/IDA-1.4.4 for ); Wed, 18 Jun 1997 04:18:53 -0500 Message-Id: <01BC7BD9.4F1AB000@rump> From: "Siegfried M. Rump" To: "'reliable_computing [at] interval [dot] usl.edu'" Subject: summer school Date: Mon, 16 Jun 1997 12:51:10 +-200 Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Sender: owner-reliable_computing Precedence: bulk =20 Dear Collegues,=20 this fall a summer school on programming languages will take place in = Hamburg. Most of the talks will be in German, therefore I continue in that language = (appologize to English-speaking=20 friends).=20 Die Sommerschule=20 "Moderne Programmiersprachen und Programmiermodelle" findet vom 15. bis 19. September in Hamburg statt. Sie richtet sich = haupts=E4chlich an Studenten und Doktoranden der Mathematik und Informatik. Behandelt werden Sprachen = f=FCr wissenschaftliches Rechnen,=20 u.a. auch Werkzeuge f=FCr verifiziertes Rechnen und = Ergebnisverifikation. Vortragssprache ist zum gr=F6=DFten Teil Deutsch. Weitere Informationen k=F6nnen unter = http://www-info2.informatik.uni-wuerzburg.de/staff/wvg/Sommer/program.htm= l abgefragt werden. Unter dieser Adresse finden sich auch = Informationen =FCber andere Sommerschulen.=20 Teilnehmer sind herzlich willkommen. U.U. kann ein Zuschu=DF zum = Aufenthalt gew=E4hrt werden.=20 Herzliche Gr=FC=DFe, with best regards, Siegfried M. Rump From owner-reliable_computing Thu Jun 19 06:38:02 1997 Received: by interval.usl.edu id AA01201 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Thu, 19 Jun 1997 01:42:25 -0500 Received: from rztsun.rz.tu-harburg.de by interval.usl.edu with SMTP id AA01195 (5.65c/IDA-1.4.4 for ); Thu, 19 Jun 1997 01:42:22 -0500 Message-Id: <01BC7C8C.AF122980@rump> From: "Siegfried M. Rump" To: "'reliable_computing [at] interval [dot] usl.edu'" Subject: WG: summer school Date: Thu, 19 Jun 1997 08:38:02 +-200 Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Sender: owner-reliable_computing Precedence: bulk =20 We had mail problems. Sorry, if you receive this twice.=20 =20 Dear Collegues,=20 this fall a summer school on programming languages will take place in = Hamburg. Most of the talks will be in German, therefore I continue in that language = (appologize to English-speaking=20 friends).=20 Die Sommerschule=20 "Moderne Programmiersprachen und Programmiermodelle" findet vom 15. bis 19. September in Hamburg statt. Sie richtet sich = haupts=E4chlich an Studenten und Doktoranden der Mathematik und Informatik. Behandelt werden Sprachen = f=FCr wissenschaftliches Rechnen,=20 u.a. auch Werkzeuge f=FCr verifiziertes Rechnen und = Ergebnisverifikation. Vortragssprache ist zum gr=F6=DFten Teil Deutsch. Weitere Informationen k=F6nnen unter = http://www-info2.informatik.uni-wuerzburg.de/staff/wvg/Sommer/program.htm= l abgefragt werden. Unter dieser Adresse finden sich auch = Informationen =FCber andere Sommerschulen.=20 Teilnehmer sind herzlich willkommen. U.U. kann ein Zuschu=DF zum = Aufenthalt gew=E4hrt werden.=20 Herzliche Gr=FC=DFe, with best regards, Siegfried M. Rump From owner-reliable_computing Thu Jun 19 18:12:46 1997 Received: by interval.usl.edu id AA01765 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Thu, 19 Jun 1997 09:08:38 -0500 Received: from mincen.emse.fr by interval.usl.edu with SMTP id AA01759 (5.65c/IDA-1.4.4 for ); Thu, 19 Jun 1997 09:08:20 -0500 Received: from maia.emse.fr by mincen.emse.fr (4.1/SMI-4.1) id AA28843; Thu, 19 Jun 97 16:07:57 +0200 Received: by maia.emse.fr (4.1/SMI-4.1) id AA27902; Thu, 19 Jun 97 16:12:46 +0200 Date: Thu, 19 Jun 97 16:12:46 +0200 From: micheluc [at] maia [dot] emse.fr (Dominique MICHELUCCI) Message-Id: <9706191412.AA27902 [at] maia [dot] emse.fr> To: reliable_computing [at] interval [dot] usl.edu Subject: RNC 98: Call for papers Sender: owner-reliable_computing Precedence: bulk CALL FOR PAPERS 3nd CONFERENCE REAL NUMBERS AND COMPUTERS Location and date Pierre et Marie Curie University Paris, FRANCE April 27-28-29 1998 The conference continues the series of RNC-symposia which have been held in St-Etienne (France, 1994) and Marseille (France, 1995). These conferences traditionally cover all the aspects in relationship with an efficient handling of real numbers on computers : program portability problems, "exact arithmetics", numerical reliability, number systems, architectures etc. Many members of the scientific community are concerned by these problems, they could share their knowledge and come up with solutions. But they do not have the opportunity to meet, they do not belong to the same scientific fields (computer science, number theory, numerical analysis, computer algebra) and they have a different vocabulary. One of the aims is to put them together during this meeting. The topics covered by the conference are - Algorithms and architectures for "serial" and "on line" arithmetic. - Relations between number theory, automata theory and computer arithmetic. - Number systems - Floating point arithmetic - Calculability - Symbolic manipulation of numbers - Algorithms for "exact" computing - Multi-precision, interval arithmetic, stochastic arithmetic ... - Accuracy problems in various fields (geometry, physics,...), and proposed solutions. DEADLINE FOR SUBMISSION OF MANUSCRIPTS January 1st 1998 You can submit a full paper (not an abstract) to: RNC3 [at] lip6 [dot] fr preferably in LaTeX. Please request a pattern LaTeX file from the above address. If you cannot use LaTeX, send 4 copies of a printed version to Jean-Marie Chesneaux Laboratoire LIP6 Universite Pierre et Marie Curie 4 place Jussieu, 75252 Paris Cedex 05, FRANCE. All informations can be found at the URL address : http://cestac.ibp.fr/RNC3/ or http://www-anp.lip6.fr/RNC3/ Any question can also be sent at the e-mail address : Jean-Marie.Chesneaux [at] lip6 [dot] fr Local committee Jean-Marie CHESNEAUX, Fabienne JEZEQUEL, Jean-Luc LAMOTTE, Jean VIGNES (LIP6, UPMC, Paris, France) Program committee Jean-Paul ALLOUCHE (France),Rene ALT (France),Jean-Claude BAJARD (France), Jean-Claude BERGES (France),Vasco BRATTKA (Germany),Jean-Marie CHESNEAUX (France), Martin Hotzel ESCARDO (United Kingdom),Christiane FROUGNY (France), Peter KORNERUP (Danmark),David LESTER (United Kingdom),Pierre LIARDET (France), Dominique MICHELUCCI (France),Jean-Michel MULLER (France),Nathalie REVOL (France) From owner-reliable_computing Fri Jun 20 07:09:54 1997 Received: by interval.usl.edu id AA03783 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Fri, 20 Jun 1997 12:09:56 -0500 Received: by interval.usl.edu id AA03773 (5.65c/IDA-1.4.4 for reliable_computing); Fri, 20 Jun 1997 12:09:54 -0500 Date: Fri, 20 Jun 1997 12:09:54 -0500 From: "Kearfott R. Baker" Message-Id: <199706201709.AA03773 [at] interval [dot] usl.edu> To: reliable_computing Subject: CFP: 1st International Workshop on Verification, Model Checking Sender: owner-reliable_computing Precedence: bulk From elena [at] oink [dot] dsi.unive.it Fri Jun 20 18:43:40 1997 From: Elena Marchiori Date: Fri, 20 Jun 97 16:43:40 +0200 X-Mts: smtp You may possibly receive this message multiple times. We apologize for the inconvenience. ---------------------------------------------------------------------------- 1st International Workshop on Verification, Model Checking and Abstract Interpretation in conjunction with ILPS'97, Port Jefferson, Long Island N.Y. Oct 12-17 1997 ---------------------------------------------------------------------------- The aim of the workshop is to bring together people working in the Program Development area and interested in the design of new tools for program development, authentication and optimization. In the past years, the concepts of verification and abstract interpretation have been widely used for the study of program properties. Model checking is a specific approach to verification which has proven successful in the area of finite-state programs. Being a general technique, it also applies to finite-state programs expressed through the logic programming paradigm, although not much research seems to exist that is specifically aimed at this integration. Verification, model checking and abstract interpretation have many similarities. The main goal of the workshop is to enhance cross-fertilization among these areas and in this way to clarify their relationship. Each area can profit from results in the others: tools, domains of applications, general results. Papers are solicitated, reporting on the use of techniques for deriving or proving properties of programs and more generally of finite dynamic systems. Contributions examining the relations among the different techniques in the field of (constraint) logic programming and other programming paradigms, will be considered particularly interesting. Description of work in progress is also welcome. Topics include but are not limited to: * optimization * verification * static analysis * model checking * debugging * tools At least one author of each accepted abstract is expected to attend the workshop. IMPORTANT DATES: Papers Submission Deadline: July 10, 1997 Notification of acceptance: July 30, 1997 Workshop : October 17, 1997 ORGANIZING COMMITTEE: Annalisa Bossi, Univ. Ca' Foscari of Venice, Italy (bossi [at] dsi [dot] unive.it) Dennis Dams, Eindhoven Univ. of Technology, The Netherlands (wsindd [at] win [dot] tue.nl) Gilberto File', University of Padova, Italy (gilberto [at] math [dot] unipd.it) Elena Marchiori, Univ. Ca' Foscari of Venice, Italy (elena [at] dsi [dot] unive.it) SUBMISSIONS: Authors are invited to submit an abstract (up to 7 pages) by e-mail in PostScript format to bossi [at] dsi [dot] unive.it If you intend to submit a paper, please inform the workshop coordinator (bossi [at] dsi [dot] unive.it) before 30 June PROCEEDINGS: The proceedings will be published as a technical report of the University Ca' Foscari of Venice, Italy, and will be available on the world-wide-web. Updated INFORMATION on the ILPS97 conference as well as on the post-conference workshops will be available at: http://www.ida.liu.se/~ilps97/ COORDINATOR ADDRESS: Annalisa Bossi University Ca' Foscari of Venice via Torino 155, 30173 Venezia-Mestre, Italy Phone: +39 (41) 2908421 Fax : +39 (41) 2908419 e-mail: bossi [at] dsi [dot] unive.it WWW: http://www.dsi.unive.it/~bossi From owner-reliable_computing Mon Jun 23 05:06:53 1997 Received: by interval.usl.edu id AA05803 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Mon, 23 Jun 1997 12:06:58 -0500 Received: from cs.utep.edu by interval.usl.edu with SMTP id AA05797 (5.65c/IDA-1.4.4 for ); Mon, 23 Jun 1997 12:06:55 -0500 Received: from earth.cs.utep.edu by cs.utep.edu (4.1/SMI-4.1) id AA13447; Mon, 23 Jun 97 11:06:53 MDT Date: Mon, 23 Jun 97 11:06:53 MDT From: vladik [at] cs [dot] utep.edu (Vladik Kreinovich) Message-Id: <9706231706.AA13447 [at] cs [dot] utep.edu> To: reliable_computing [at] interval [dot] usl.edu Subject: a question of Elishakoff Cc: ielishak [at] me [dot] fau.edu Sender: owner-reliable_computing Precedence: bulk Dr. Elishakoff is currently writing a paper on interval computations, and he is interested in the history of interval analysis, who were the first authors who intriduced intervals in their analysis. Of course, we can always call Archimedes the first interval person, but there may be more direct connections for older authors. This question is of definite interest to the community in general. Please respond to him, his email is on the list. Vladik From owner-reliable_computing Tue Jun 24 02:53:33 1997 Received: by interval.usl.edu id AA06863 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Tue, 24 Jun 1997 07:53:36 -0500 Received: by interval.usl.edu id AA06853 (5.65c/IDA-1.4.4 for reliable_computing); Tue, 24 Jun 1997 07:53:33 -0500 Date: Tue, 24 Jun 1997 07:53:33 -0500 From: "Kearfott R. Baker" Message-Id: <199706241253.AA06853 [at] interval [dot] usl.edu> To: reliable_computing Subject: Re: linear systems - Help Sender: owner-reliable_computing Precedence: bulk ----- Begin Included Message ----- From Franck.DELCROIX [at] devinci [dot] fr Tue Jun 24 03:14:01 1997 From: "Franck DELCROIX" Date: Tue, 24 Jun 1997 10:13:41 +0000 Reply-To: franck.delcroix [at] devinci [dot] fr X-Mailer: Z-Mail (3.2.0 26oct94 MediaMail) To: owner-reliable_computing [at] interval [dot] usl.edu Subject: linear systems - Help X-Zm-Priority: High Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Length: 1452 Dear Interval Researchers, My question concerns the solution of linear systmes of equations with interval coefficients. Let's consider a linear system AX=B where Aij and Bi coefficients are functions of N interval variables. That is : A(y1,...,yN) X = B(y1,...,yN) (1) - Solving (1) for X is possible in some (rare) cases using methods presented in "classical" interval litterature (e.g. Alefeld, Hansen, ...) (By the way, why the examples treated in all the papers and books dealing with interval linear systems do not consider problems of dimension higher than 4 ??? Does it means it's unfeasible ??? Some hints ???) - But, I recently read a paper where they consider the N-dimensional volume defined by the 2*N end-points of the interval (y1,...,yN). Then they solve classically AX=B for the 2^N possible realisations and sort the answers. Hence, X is [min(Xi) ; max(Xi)] where i stands for one of the realisations amongst the 2^N possible combinations of the 2*N end-points. Is that method correct ??? I think the answer of this question deals with the monotonicity of X with respect to (y1,...,yN) but I can't express clearly that point ... ( Moreover, this method would lead to huge computations if we consider large scale systems with high number of interval variables (large N) ) Any help and ideas welcome, Thanks very much, Franck (PhD student, Paris - France). ----- End Included Message ----- From owner-reliable_computing Tue Jun 24 18:15:22 1997 Received: by interval.usl.edu id AA10610 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Tue, 24 Jun 1997 12:21:08 -0500 Received: from Pap.UniVie.AC.AT (apap4.pap.univie.ac.at) by interval.usl.edu with SMTP id AA10602 (5.65c/IDA-1.4.4 for ); Tue, 24 Jun 1997 12:20:50 -0500 Received: from homer.cma.univie.ac.at by Pap.UniVie.AC.AT (PMDF V5.0-4 #10670) id <01IKGGJNWBI8E0L4IP [at] Pap [dot] UniVie.AC.AT>; Tue, 24 Jun 1997 16:14:55 +0100 (MET) Received: by homer.cma.univie.ac.at (5.65v3.2/1.1.10.5/19Mar97-1148AM) id AA26527; Tue, 24 Jun 1997 16:15:22 +0200 Date: Tue, 24 Jun 1997 16:15:22 +0200 From: Arnold Neumaier Subject: Re: linear systems - Help To: rbk5287 [at] interval [dot] usl.edu, reliable_computing [at] interval [dot] usl.edu Cc: neum [at] homer [dot] cma.univie.ac.at Message-Id: <9706241415.AA26527 [at] homer [dot] cma.univie.ac.at> Content-Transfer-Encoding: 7BIT Sender: owner-reliable_computing Precedence: bulk Franck wrote: >> To solve ... A(y1,...,yN) X = B(y1,...,yN) ... they solve classically AX=B for the 2^N possible realisations and sort the answers. Hence, X is [min(Xi) ; max(Xi)] where i stands for one of the realisations amongst the 2^N possible combinations of the 2*N end-points. << This is correct only if the partial derivatives of X with respect to (y1,...,yN) have constant sign; but to check this one needs an enclosure of the inverse matrix. Hansen has written something about this in case the y_i are coefficients of A or B, but this approach generalizes. I don't remerber the reference, but it should be in the interval bibliography available from http://solon.cma.univie.ac.at/~neum/interval.html Arnold Neumaier From owner-reliable_computing Tue Jun 24 22:58:36 1997 Received: by interval.usl.edu id AA12240 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Tue, 24 Jun 1997 13:38:43 -0500 Received: from iph.bio.acad.bg ([194.141.4.1]) by interval.usl.edu with SMTP id AA12234 (5.65c/IDA-1.4.4 for ); Tue, 24 Jun 1997 13:38:24 -0500 Received: from biomath.bio.acad.bg (biomath.bio.acad.bg [194.141.4.32]) by iph.bio.acad.bg (8.7.1/8.7.1) with SMTP id VAA00634; Tue, 24 Jun 1997 21:34:40 +0300 Message-Id: <199706241834.VAA00634 [at] iph [dot] bio.acad.bg> Comments: Authenticated sender is From: "Svetoslav Markov" Organization: Institute of Biophysics - BAS To: reliable_computing [at] interval [dot] usl.edu Date: Tue, 24 Jun 1997 20:58:36 +0200 Subject: Re: linear systems - Help Reply-To: smarkov [at] iph [dot] bio.acad.bg Cc: Franck.DELCROIX [at] devinci [dot] fr X-Confirm-Reading-To: smarkov [at] iph [dot] bio.acad.bg X-Pmrqc: 1 Priority: normal X-Mailer: Pegasus Mail for Windows (v2.23) Sender: owner-reliable_computing Precedence: bulk > > My question concerns the solution of linear systmes of equations with interval > coefficients. > > Let's consider a linear system AX=B where Aij and Bi coefficients are > functions of N interval variables. That is : > > A(y1,...,yN) X = B(y1,...,yN) (1) > > Solving (1) for X is possible in some (rare) cases using methods presented > in "classical" interval literature (e.g. Alefeld, Hansen, ...) > As far as I understand by solving (1) you mean finding tight (inner and outer) enclosures for the set of solutions of all (real) systems (1) whenever y1,...,yN vary in presribed intervals Y1, ..., YN. My comments are related to this problem, which seems to be a very important problem from applicational point of view. A more simple variant of problem (1) is the problem (2): find tight (inner and outer) (interval) enclosures of a rational function depending on N variables tracing prescribed intervals. It is my opinion that a proper tool for solving problems (1) and (2) is extended interval arithmetic. There are some results concerning problem (2) by V. Nesterov, N. Dimitrova and myself (using exended interval arithmetic). For problem (1) there is almost nothing and I do not beleive that there will be soon general results. As you mention, monotonicity plays important role, therefore successful treatment can be expected (at least in the beginning) only for certain classes of problems, arrising from applications, where monotonicities are present. I have considered a simple case of problem (1) when N=1 and A is a matrix of constant numbers; this problem arised from the problem of smooting al function depending on an interval parameter (see S. Markov, Some interpolation problems involving interval data, Interval Computations, 3 (1993), 164--182). I am now working on a problem where both A and B are functions on one parameter (for which an interval is prescribed). > > I think the answer of this question deals with the monotonicity of X with > respect to (y1,...,yN) but I can't express clearly that point ... > Yes. However, "to express clearly that point" is not trivial. To my knowledge the first who formulated the problem of finding the range of a function depending monotonically on many variables was K. Nickel. S. Markov -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + Dr. Svetoslav Markov Section "Biomathematics", Inst. of phone: +3592-713-3704, +3592-707460, Mathematics and Computer Sci., fax: +3592-971-3649, +3592-707273 Bulgarian Academy of Sciences, e-mail: smarkov [at] iph [dot] bio.acad.bg "Acad. G. Bonchev" st., block 8, smarkov [at] bgearn [dot] bitnet, BG-1113 Sofia, BULGARIA smarkov [at] bgearn [dot] acad.bg home address: 11 Mizia, 1124 Sofia, tel. +3592-444651 -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + -- + From owner-reliable_computing Wed Jun 25 02:49:19 1997 Received: by interval.usl.edu id AA13141 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Wed, 25 Jun 1997 07:49:21 -0500 Received: by interval.usl.edu id AA13131 (5.65c/IDA-1.4.4 for reliable_computing); Wed, 25 Jun 1997 07:49:19 -0500 Date: Wed, 25 Jun 1997 07:49:19 -0500 From: "Kearfott R. Baker" Message-Id: <199706251249.AA13131 [at] interval [dot] usl.edu> To: reliable_computing Subject: CP97 Workshop on Constraint Reasoning on the Internet Sender: owner-reliable_computing Precedence: bulk ----- Begin Included Message ----- From: Thom Fruehwirth Date: Wed, 25 Jun 97 13:37:05 +0200 Subject: CP97 Workshop on Constraint Reasoning on the Internet We apologize for multiple copies. CALL FOR PAPERS CP97 Workshop on Constraint Reasoning on the Internet Schloss Hagenberg, Austria, 1 November 1997 The half-day workshop will be held in conjunction with the Third International Conference on Principles and Practice of Constraint Programming (CP97), October 29 - November 1, 1997 SCOPE OF THE WORKSHOP Constraint reasoning has proven its merits in a variety of application areas including decision support systems. The goal of the workshop is to assess whether and in what way constraint reasoning and programming may be applied to developing intelligent applications for the Web including agent-based systems. We believe that constraint-based programming will be essential for intelligent internet applications, be they called intelligent information systems, intelligent agents, etc. The reason is that since constraints can express and deal with partial information, they address some of the essential issues of intelligent applications on the WWW: - Internet applications are likely to be distributed and thus, locally, complete information may not be available at all times. - The internet user may not be able to give all the necessary input, but still expect to get some answer. - The internet user may not want to reveal all he knows to an application for security or privacy reasons. Topics of interest include, but are not limited to: - internet applications - intelligent agents - WWW interfaces, interactivity - user-specific content presentation, on-the-fly web page creation - CLP-applets and internet libraries - what do existing LP libraries offer? - internet information search, data mining and information retrieval - decision support systems that can/should be put on the internet - concurreny and distributed computing w.r.t. internet Papers that combine theory and practice are especially welcome. PAPER SUBMISSIONS Submission deadline is 7 August 1997. Authors are invited to submit original papers written in English with up to 10 A4 pages by electronic mail in self-contained uuencoded Postscript format to Thom Fruehwirth at fruehwir [at] informatik [dot] uni-muenchen.de. Decisions on acceptance will be sent to authors by 19 September 1997. PUBLICATION An informal proceedings of the workshop will be available to the workshop participants. Final copies will be due by 5 October 1997. ORGANISATION Thom Fruehwirth, LMU Munich, Germany, fruehwir [at] informatik [dot] uni-muenchen.de Manuel Hermengildo, Univ. Politecnica de Madrid, Spain, herme [at] fi [dot] upm.es Paul Tarau, Univ. de Moncton, Canada, tarau [at] info [dot] umoncton.ca Philippe Codognet, INRIA, France, Philippe.Codognet [at] inria [dot] fr Francesca Rossi, Univ. di Pisa, Italy, rossi [at] di [dot] unipi.it IMPORTANT DATES 7 August 1997: Paper submissions (by email only) 19 September 1997: Acceptance decisions 5 October 1997: Final copy due 1 November 1997: Workshop FURTHER INFORMATION This and more information related to the topic of the workshop may be found in the internet at URL: http://www.pst.informatik.uni-muenchen.de/personen/fruehwir/wcicp97.html Thom Fruehwirth ----- End Included Message ----- From owner-reliable_computing Wed Jun 25 10:48:33 1997 Received: by interval.usl.edu id AA13997 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Wed, 25 Jun 1997 15:48:36 -0500 Received: by interval.usl.edu id AA13987 (5.65c/IDA-1.4.4 for reliable_computing); Wed, 25 Jun 1997 15:48:33 -0500 Date: Wed, 25 Jun 1997 15:48:33 -0500 From: "Kearfott R. Baker" Message-Id: <199706252048.AA13987 [at] interval [dot] usl.edu> To: reliable_computing Subject: Errata for "Rigorous Global Search" available Sender: owner-reliable_computing Precedence: bulk My student, Jianwei Dian, has read Chapter 1 of my book, "Rigorous Global Search: Continuous Problems" very carefully, and has compiled a list of corrections, some of which are significant. I have placed these corrections at the URL's: http://interval.usl.edu/books/errata_ch_1.ps (Postscript) and http://interval.usl.edu/books/errata_ch_1.dvi (TeX DVI) I recommend that you receive and print this errata, especially if you intend to use this book as a text. This is because some of the corrections concern examples in the introductory material, and the errors could cause confusion. I remind you that a table of contents, preface, index, and order form for the book can be found from my home page at http://interval.usl.edu/kearfott.html by clicking on the "global optimization book" item at the top of the page. Best regards, Baker --------------------------------------------------------------- R. Baker Kearfott, rbk [at] usl [dot] edu (318) 482-5346 (fax) (318) 482-5270 (work) (318) 981-9744 (home) URL: http://interval.usl.edu/kearfott.html Department of Mathematics, University of Southwestern Louisiana --------------------------------------------------------------- From owner-reliable_computing Wed Jun 25 09:28:58 1997 Received: by interval.usl.edu id AA14364 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Wed, 25 Jun 1997 16:29:11 -0500 Received: from cs.utep.edu by interval.usl.edu with SMTP id AA14358 (5.65c/IDA-1.4.4 for ); Wed, 25 Jun 1997 16:29:01 -0500 Received: from earth.cs.utep.edu by cs.utep.edu (4.1/SMI-4.1) id AA29970; Wed, 25 Jun 97 15:28:58 MDT Date: Wed, 25 Jun 97 15:28:58 MDT From: vladik [at] cs [dot] utep.edu (Vladik Kreinovich) Message-Id: <9706252128.AA29970 [at] cs [dot] utep.edu> To: reliable_computing [at] interval [dot] usl.edu Subject: Book using interval methods Sender: owner-reliable_computing Precedence: bulk From prior [at] MIT [dot] EDU Wed Jun 25 10:43:15 1997 The MIT Press has recently published a book of interest to the Interval Computations community. The book is *Numerica: A Modeling Language for Global Optimization* by Pascal Van Hentenryck, Laurent Michel, and Yves Deville. Numerica is modeling language for global optimization that makes it possible to state nonlinear problems in a form close to the statements traditionally found in textbooks and scientific papers. The constraint-solving algorithm of Numerica is based on a combination of traditional numerical methods such as interval and local methods, and constraint satisfaction techniques. More information can be found at the book's homepage: http://www-mitpress.mit.edu/book-home.tcl?isbn=0262720272 ROBERT V. PRIOR Computer Science Editor prior [at] mit [dot] edu The MIT Press (617) 253-1584 Five Cambridge Center Fax: (617) 258-6779 Cambridge, MA 02142 http://mitpress.mit.edu/ ----- End Included Message ----- From owner-reliable_computing Mon Jun 30 10:07:44 1997 Received: by interval.usl.edu id AA18384 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Mon, 30 Jun 1997 05:08:38 -0500 Received: from rztsun.rz.tu-harburg.de by interval.usl.edu with SMTP id AA18376 (5.65c/IDA-1.4.4 for ); Mon, 30 Jun 1997 05:08:34 -0500 Message-Id: <01BC854E.42C855E0@rump> From: "Siegfried M. Rump" To: "'Kearfott R. Baker'" Cc: "'reliable_computing [at] interval [dot] usl.edu'" Subject: AW: linear systems - Help Date: Mon, 30 Jun 1997 12:07:44 +-200 Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing Precedence: bulk ---------- Von: Kearfott R. Baker[SMTP:rbk5287 [at] interval [dot] usl.edu] Gesendet: Dienstag, 24. Juni 1997 14:53 An: reliable_computing [at] interval [dot] usl.edu Betreff: Dear Interval Researchers, My question concerns the solution of linear systmes of equations with interval coefficients. Let's consider a linear system AX=B where Aij and Bi coefficients are functions of N interval variables. That is : A(y1,...,yN) X = B(y1,...,yN) (1) - Solving (1) for X is possible in some (rare) cases using methods presented in "classical" interval litterature (e.g. Alefeld, Hansen, ...) (By the way, why the examples treated in all the papers and books dealing with interval linear systems do not consider problems of dimension higher than 4 ??? Does it means it's unfeasible ??? Some hints ???) Yes, Baker. Look in my papers. largest dimension treated is 1 000 000. - But, I recently read a paper where they consider the N-dimensional volume defined by the 2*N end-points of the interval (y1,...,yN). Then they solve classically AX=B for the 2^N possible realisations and sort the answers. Hence, X is [min(Xi) ; max(Xi)] where i stands for one of the realisations amongst the 2^N possible combinations of the 2*N end-points. Is that method correct ??? I think the answer of this question deals with the monotonicity of X with respect to (y1,...,yN) but I can't express clearly that point ... See Arnold's message. ( Moreover, this method would lead to huge computations if we consider large scale systems with high number of interval variables (large N) ) Any help and ideas welcome, Thanks very much, Franck (PhD student, Paris - France). Best regards, Siegfried From owner-reliable_computing Mon Jun 30 05:17:01 1997 Received: by interval.usl.edu id AA18699 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Mon, 30 Jun 1997 08:18:41 -0500 Received: from graf.cc.emory.edu by interval.usl.edu with SMTP id AA18693 (5.65c/IDA-1.4.4 for ); Mon, 30 Jun 1997 08:18:38 -0500 Received: from larry.cc.emory.edu (vrorie [at] larry [dot] cc.emory.edu [170.140.1.65]) by graf.cc.emory.edu (8.7.3/8.6.9-950630.01osg-itd.null) with SMTP id JAA19518; Mon, 30 Jun 1997 09:15:04 -0400 (EDT) Date: Mon, 30 Jun 1997 09:17:01 -0400 (EDT) From: Vera Dixon Rorie X-Sender: vrorie [at] larry [dot] cc.emory.edu To: "Siegfried M. Rump" Cc: "'Kearfott R. Baker'" , "'reliable_computing [at] interval [dot] usl.edu'" Subject: Re: AW: linear systems - Help In-Reply-To: <01BC854E.42C855E0@rump> Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: owner-reliable_computing Precedence: bulk please unscribe me from this computing program. V. Rorie v r On Mon, 30 Jun 1997, Siegfried M. Rump wrote: > > > ---------- > Von: Kearfott R. Baker[SMTP:rbk5287 [at] interval [dot] usl.edu] > Gesendet: Dienstag, 24. Juni 1997 14:53 > An: reliable_computing [at] interval [dot] usl.edu > Betreff: > > > Dear Interval Researchers, > > My question concerns the solution of linear systmes of equations with interval > coefficients. > > Let's consider a linear system AX=B where Aij and Bi coefficients are > functions of N interval variables. That is : > > A(y1,...,yN) X = B(y1,...,yN) (1) > > > - Solving (1) for X is possible in some (rare) cases using methods presented > in "classical" interval litterature (e.g. Alefeld, Hansen, ...) > > (By the way, why the examples treated in all the papers and books dealing > with interval linear systems do not consider problems of dimension higher > than 4 ??? Does it means it's unfeasible ??? Some hints ???) > > > Yes, Baker. Look in my papers. largest dimension treated is 1 000 000. > > - But, I recently read a paper where they consider the N-dimensional volume > defined by the 2*N end-points of the interval (y1,...,yN). Then they solve > classically AX=B for the 2^N possible realisations and sort the answers. > Hence, X is [min(Xi) ; max(Xi)] where i stands for one of the realisations > amongst the 2^N possible combinations of the 2*N end-points. > > > Is that method correct ??? > > I think the answer of this question deals with the monotonicity of X with > respect to (y1,...,yN) but I can't express clearly that point ... > > See Arnold's message. > > ( Moreover, this method would lead to huge computations if we consider large > scale systems with high number of interval variables (large N) ) > > > Any help and ideas welcome, > > > Thanks very much, > > Franck (PhD student, Paris - France). > > > Best regards, Siegfried > From owner-reliable_computing Mon Jun 30 07:55:51 1997 Received: by interval.usl.edu id AA19523 (5.65c/IDA-1.4.4 for reliable_computing-outgoing); Mon, 30 Jun 1997 15:10:19 -0500 Received: from cs.utep.edu by interval.usl.edu with SMTP id AA19517 (5.65c/IDA-1.4.4 for ); Mon, 30 Jun 1997 15:10:13 -0500 Received: from earth.cs.utep.edu by cs.utep.edu (4.1/SMI-4.1) id AA17376; Mon, 30 Jun 97 13:55:51 MDT Date: Mon, 30 Jun 97 13:55:51 MDT From: vladik [at] cs [dot] utep.edu (Vladik Kreinovich) Message-Id: <9706301955.AA17376 [at] cs [dot] utep.edu> To: reliable_computing [at] interval [dot] usl.edu, Franck.DELCROIX [at] devinci [dot] fr Subject: Re: linear systems - Help Sender: owner-reliable_computing Precedence: bulk > My question concerns the solution of linear systmes of equations > with interval coefficients. > - But, I recently read a paper where they consider the N-dimensional volume > defined by the 2*N end-points of the interval (y1,...,yN). Then they solve > classically AX=B for the 2^N possible realisations and sort the answers. > Hence, X is [min(Xi) ; max(Xi)] where i stands for one of the realisations > amongst the 2^N possible combinations of the 2*N end-points. > Is that method correct ??? Not necessarily: e.g., for a single equation [-1,1]x=[0,1], the four points are 0, 1, and -1, so we should expect the interval to be [-1,1], but in reality, possible values of x form the entire real line. It is easy to modify this result and make it non-trivial. > (Moreover, this method would lead to huge computations if we consider large > scale systems with high number of interval variables (large N) ) Not only this method: there is a theorem that the problem of solving systems of linear interval equations is NP-hard. Crudely speaking, this means that whatever algorithm we use for computing the exact interval bounds for xi, for *some* systems this method will require exponential time.