Interval arithmetic library in BOOST

*************************************************=0A=

From: =0A= Brigitte Verdonk <brigitte.verdonk [at] ua [dot] ac.be>
Date: Sat, 6 Aug = 2005 =0A= 06:23:03 +0200 (CEST)
Subject: Mini-symposium at ICNAAM on the = Computation of =0A= Special Functions

Due to the great interest for ICNAAM 2005 =0A= (International Conference on
Numerical Analysis and Applied = Mathematics), the =0A= deadline for
participation and registration has been extended. We = invite =0A= late
submissions for the =0A= mini-symposium

ON THE =0A= COMPUTATION OF SPECIAL FUNCTIONS

organized at ICNAAM =0A= 2005.

Mini-symposium topic:

Because of the importance of = special =0A= functions, many of their properties,
developed over the centuries, = have been =0A= collected in formula books.
Since the 1960s, also algorithms and = software for =0A= the approximation of
special functions have been developed and =0A= published. Many collections
are available now: on the = Internet, =0A= in books, in software systems
such as MATLAB, NAG and IMSL, and in = computer =0A= algebra packages such as
Maple and Mathematica, to mention important = (but not =0A= all) examples.

However, there is a persistent need for numerical =0A= algorithms for all
kinds of special functions. It is the aim of the =0A= mini-symposium to bring
together several experts on this topic. = Recent =0A= results on the numerical
computation of special functions will be =0A= presented.

Invited speakers (in alphabetical order):

Dirk = Laurie, =0A= Nico Temme, Andre Weideman

Organizers:

Annie Cuyt =0A= (annie.cuyt [at] ua [dot] ac.be), Brigitte =0A= Verdonk
(brigitte.verdonk [at] ua [dot] ac.be)

Abstracts should be sent = directly =0A= to the mini-symposium organizers.
For details on submission deadlines = and =0A= registration, please refer = to

=0A= http://www.uop.gr/~icnaam

------_=_NextPart_001_01C59BD2.161BF44A-- From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Aug 9 14:15:49 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j79JFm3H013932 for ; Tue, 9 Aug 2005 14:15:48 -0500 (CDT) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j79JFmHX013931 for reliable_computing-outgoing; Tue, 9 Aug 2005 14:15:48 -0500 (CDT) Received: from poczta.polsl.pl (castor.polsl.pl [157.158.3.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j79JFcME013927 for ; Tue, 9 Aug 2005 14:15:44 -0500 (CDT) X-MimeOLE: Produced By Microsoft Exchange V6.5.7226.0 Content-class: urn:content-classes:message MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----_=_NextPart_001_01C59D16.B02C61C6" Subject: Web-applications related to equations with interval parameters Date: Tue, 9 Aug 2005 21:15:22 +0200 Message-ID: <0FD17B3AD1251C40A9ED696128062BF1927D9D [at] castor [dot] polsl.pl> X-MS-Has-Attach: X-MS-TNEF-Correlator: Thread-Topic: Web-applications related to equations with interval parameters thread-index: AcWdFq/imZ3vtDnFRpubQE+3gTnLWA== From: "Andrzej Pownuk" To: Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. ------_=_NextPart_001_01C59D16.B02C61C6 Content-Type: text/plain; charset="iso-8859-2" Content-Transfer-Encoding: quoted-printable Dear members of this group, On the following web page =20 http://pownuk.prv.pl/interval_web_applications.htm There are web applications which calculate displacements=20 of truss structures with interval parameters.=20 Binary version of the program is also included. Additionally there is a solution program which calculates=20 of non-stationary diffusion equations with interval parameters.=20 =20 The algorithms of calculations are based on sensitivity analysis=20 and gives only approximate results=20 but maybe some members of this group=20 will be interested of the results,=20 which are generated by these programs just for comparison. 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 =20 Tel/fax: 0048 32 2371542=20 Mobile: 0048 606 550147=20 URL: http://pownuk.com E-mail: andrzej [at] pownuk [dot] com --------------------------------------------- ------_=_NextPart_001_01C59D16.B02C61C6 Content-Type: text/html; charset="iso-8859-2" Content-Transfer-Encoding: quoted-printable =0A=

Dear members of this group,

=0A=

On the following web page

http://pownuk= .prv.pl/interval_web_applications.htm

=0A=

There are web applications which calculate displacements
of truss =0A= structures with interval parameters.
Binary version of the program = is also =0A= included.
Additionally there is a solution program which calculates =
of =0A= non-stationary diffusion equations with interval parameters. =

=0A=

The algorithms of calculations are based on sensitivity analysis =
and =0A= gives only approximate results
but maybe some members of this group =
will =0A= be interested of the results,
which are generated by these programs = just for =0A= comparison.

=0A=

Regards,

=0A=

Andrzej Pownuk

=0A=

---------------------------------------------
Ph.D., research = associate =0A= at:
Chair of Theoretical Mechanics
Faculty of Civil =0A= Engineering
Silesian University of Technology
ul. Krzywoustego =0A= 7
44-100 Gliwice, Poland

Tel/fax: 0048 32 2371542 =0A=
Mobile: 0048 606 550147

=0A=

URL: http://pownuk.com
E-mail: andrzej [at] pownuk [dot] com
------------= ---------------------------------

------_=_NextPart_001_01C59D16.B02C61C6-- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Aug 10 04:37:29 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7A9bTgU015258 for ; Wed, 10 Aug 2005 04:37:29 -0500 (CDT) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j7A9bSed015257 for reliable_computing-outgoing; Wed, 10 Aug 2005 04:37:28 -0500 (CDT) Received: from ccsmta3.resource.rmcs.cranfield.ac.uk (ccsmta3.rmcs.cranfield.ac.uk [193.63.243.26]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7A9bE15015253 for ; Wed, 10 Aug 2005 04:37:25 -0500 (CDT) Received: from isepryce.staff.rmcs.cranfield.ac.uk ([10.4.49.11]) by ccsmta3.resource.rmcs.cranfield.ac.uk with esmtp (Exim 4.41) id 1E2n0V-00017c-OX for reliable_computing [at] interval [dot] louisiana.edu; Wed, 10 Aug 2005 10:36:19 +0100 X-Sender: prycej [at] pop3 [dot] rmcs.cranfield.ac.uk Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Wed, 10 Aug 2005 10:40:18 +0100 To: reliable_computing [at] interval [dot] louisiana.edu From: Dr John D Pryce Subject: Re: Verification and Validation X-DEFAC-MailScanner-Information: Please contact postmaster [at] rmcs [dot] cranfield.ac.uk for more information X-DEFAC-MailScanner: Found to be clean X-DEFAC-MailScanner-SpamCheck: not spam, SpamAssassin (score=0, required 6) X-MailScanner-From: j.d.pryce [at] cranfield [dot] ac.uk Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear all On the current discussion about terms & names: (1) --------------------- I have had the job of teaching our basic Software Engineering course for some years now. The distinction made by the software engineering (and I believe more broadly systems engineering) community between Verification and Validation is quite explicit: Verification: "Are we building the product right?" The software should conform to its specification. Validation: "Are we building the right product?" The software should do what the user really requires. (see e.g. "Software Engineering", Ian Sommerville, 6th edition, Chapter 19) So verification is *in principle* automatable, being about the equivalence between one formal system (a spec) and another (a software system). Validation is *in principle* non-automatable, being about the correspondence between human requirements and a formal system. This is clearly related to, but not the same as, the distinction being made in other engineering disciplines as e.g. quoted by Ray Moore in his original posting: >Evidently "validation" is widely used to refer to agreement with physical >effects, experimental results, etc. I do not think we should get too worried about "right" usage of these words, seeing that there are various communities out there that use them in subtly different ways. (2) --------------------- I am perfectly happy with the name "Reliable Computing". I think "Interval Arithmetic" and "Interval Computing" are too narrow for the reasons Baker has just given, namely you don't need intervals to get, ermm, validated results. Example: Years ago I refereed a joint paper by two great men, Jim Wilkinson and Frank Olver, on an algorithm and its implementation, for solving a (dense) linear system Ax=b with rigorous bounds on the error. This was in the days when double precision was far slower than single, and before IEEE754 I think. They just used the Wilkinson model x OP y = (1 + e) ( x op y), |e| <= u (*) where op is an exact arithmetic operation, OP is as done on the machine, u is the roundoff unit. (I think they even put in an extra term to handle underflow.) So, the scheme was to do the main computation in double precision, and simultaneously in single precision perform a running rigorous error bound of each operation (*), using an inflation of each absolute-value bound by a factor (1+u1) where u1 is the S.P. roundoff unit, so as to account for errors in the S.P. computation. You thus did Wilkinson's backward error analysis but with far sharper bounds, which in theory would be asymptotically optimal as u -> 0. So, totally "validated" but with no interval arithmetic! Wilkinson wrote me to the effect that this was Olver's baby, he found it rather boring and he could have done it on the pilot ACE in 1948 if he had really wanted to. He was much more interested in error analysis for giving insight rather than rigorous bounds. But times and needs change. --------------------- John Pryce Dr John D Pryce Lecturer in Mathematical Software Engineering Computer Information Systems Engineering Dept Cranfield University, RMCS Shrivenham Swindon SN6 8LA, UK Tel +44 (0)1793-785683 direct, +44 (0)1793-785931 secretaries, +44 (0)1793-785366 fax -- This message has been scanned for viruses and dangerous content by the Cranfield MailScanner, and is believed to be clean. From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Aug 10 09:16:22 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7AEGL3A015710 for ; Wed, 10 Aug 2005 09:16:21 -0500 (CDT) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j7AEGLrk015709 for reliable_computing-outgoing; Wed, 10 Aug 2005 09:16:21 -0500 (CDT) Received: from grpws1.uca.edu (grpws1.uca.edu [161.31.24.26]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7AEGCYH015705 for ; Wed, 10 Aug 2005 09:16:18 -0500 (CDT) Received: from GWDMN1-MTA by grpws1.uca.edu with Novell_GroupWise; Wed, 10 Aug 2005 09:16:05 -0500 Message-Id: X-Mailer: Novell GroupWise Internet Agent 6.5.4 Date: Wed, 10 Aug 2005 09:15:38 -0500 From: "Chenyi Hu" To: , Subject: Re: Verification and Validation Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Disposition: inline Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by interval.louisiana.edu id j7AEGIYH015706 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear All, I still feel very strongly that Ray's original post on this topic has great intrinsic merit. Although achieving computational reliability has been one of the most important applications of interval computing, intervals have been applied in much broader areas nowadays. Yes, there are other methods to achieve computational reliability. But, the term "interval computing" covers much more application areas than only on "verification" and validation". As a very recent example, I do not feel if it is very appropriate to submit one of our current research results on interval fuzzy decision making systems to the Journal of Reliable Computing simply because of that our work does not fit the term "Reliable". I think, the most common interests of this group probably are in interval computing and its applications. If that is true, then the term "interval computing" might not be "too narrow" for this group as it seems. Regards, Chenyi Hu >>> Dr John D Pryce 08/10/05 2:40 AM >>> Dear all On the current discussion about terms & names: (1) --------------------- I have had the job of teaching our basic Software Engineering course for some years now. The distinction made by the software engineering (and I believe more broadly systems engineering) community between Verification and Validation is quite explicit: Verification: "Are we building the product right?" The software should conform to its specification. Validation: "Are we building the right product?" The software should do what the user really requires. (see e.g. "Software Engineering", Ian Sommerville, 6th edition, Chapter 19) So verification is *in principle* automatable, being about the equivalence between one formal system (a spec) and another (a software system). Validation is *in principle* non-automatable, being about the correspondence between human requirements and a formal system. This is clearly related to, but not the same as, the distinction being made in other engineering disciplines as e.g. quoted by Ray Moore in his original posting: >Evidently "validation" is widely used to refer to agreement with physical >effects, experimental results, etc. I do not think we should get too worried about "right" usage of these words, seeing that there are various communities out there that use them in subtly different ways. (2) --------------------- I am perfectly happy with the name "Reliable Computing". I think "Interval Arithmetic" and "Interval Computing" are too narrow for the reasons Baker has just given, namely you don't need intervals to get, ermm, validated results. Example: Years ago I refereed a joint paper by two great men, Jim Wilkinson and Frank Olver, on an algorithm and its implementation, for solving a (dense) linear system Ax=b with rigorous bounds on the error. This was in the days when double precision was far slower than single, and before IEEE754 I think. They just used the Wilkinson model x OP y = (1 + e) ( x op y), |e| <= u (*) where op is an exact arithmetic operation, OP is as done on the machine, u is the roundoff unit. (I think they even put in an extra term to handle underflow.) So, the scheme was to do the main computation in double precision, and simultaneously in single precision perform a running rigorous error bound of each operation (*), using an inflation of each absolute-value bound by a factor (1+u1) where u1 is the S.P. roundoff unit, so as to account for errors in the S.P. computation. You thus did Wilkinson's backward error analysis but with far sharper bounds, which in theory would be asymptotically optimal as u -> 0. So, totally "validated" but with no interval arithmetic! Wilkinson wrote me to the effect that this was Olver's baby, he found it rather boring and he could have done it on the pilot ACE in 1948 if he had really wanted to. He was much more interested in error analysis for giving insight rather than rigorous bounds. But times and needs change. --------------------- John Pryce Dr John D Pryce Lecturer in Mathematical Software Engineering Computer Information Systems Engineering Dept Cranfield University, RMCS Shrivenham Swindon SN6 8LA, UK Tel +44 (0)1793-785683 direct, +44 (0)1793-785931 secretaries, +44 (0)1793-785366 fax -- This message has been scanned for viruses and dangerous content by the Cranfield MailScanner, and is believed to be clean. From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Aug 10 12:13:59 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7AHDxBr016466 for ; Wed, 10 Aug 2005 12:13:59 -0500 (CDT) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j7AHDw3g016465 for reliable_computing-outgoing; Wed, 10 Aug 2005 12:13:58 -0500 (CDT) Received: from cs.clemson.edu (plato.cs.clemson.edu [130.127.48.6]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7AHDnVZ016461 for ; Wed, 10 Aug 2005 12:13:55 -0500 (CDT) Received: from [130.127.49.168] (csdhcp24.cs.clemson.edu [130.127.49.168]) by cs.clemson.edu (8.13.3/8.13.3) with ESMTP id j7AHDcaM029587; Wed, 10 Aug 2005 13:13:43 -0400 (EDT) Mime-Version: 1.0 Message-Id: In-Reply-To: References: Date: Wed, 10 Aug 2005 13:13:33 -0400 To: "Chenyi Hu" , , From: Steve Stevenson Subject: Re: Verification and Validation Content-Type: text/plain; charset="us-ascii" ; format="flowed" X-Scanned-By: MIMEDefang 2.51 on 130.127.48.6 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk For what it's worth, I agree with Chenyi. I call your attention to a really interesting volume of @Proceedings{helton04, title = {Special Issue: Alternative Representations of Epistemic Uncertainty}, year = 2004, editor = {J. C. Helton and W. L. Oberkampf}, volume = 85, series = {Reliability Engineering \& System Safety}, publisher = {Elsevier} } Not only is this published in a series of reliability but the volume itself covers a large number of alternative arithmetic systems, many based in part on interval arithmetic. I think this idea is just gaining speed that alternative approaches are needed. steve At 9:15 -0500 8/10/05, Chenyi Hu wrote: >Dear All, > >I still feel very strongly that Ray's original post on this topic >has great intrinsic merit. Although achieving computational >reliability has been one of the most important applications of >interval computing, intervals have been applied in much broader >areas nowadays. Yes, there are other methods to achieve >computational reliability. But, the term "interval computing" covers >much more application areas than only on "verification" and >validation". As a very recent example, I do not feel if it is very >appropriate to submit one of our current research results on >interval fuzzy decision making systems to the Journal of Reliable >Computing simply because of that our work does not fit the term >"Reliable". I think, the most common interests of this group >probably are in interval computing and its applications. If that is >true, then the term "interval computing" might not be "too narrow" >for this group as it seems. > >Regards, > >Chenyi Hu > >>>> Dr John D Pryce 08/10/05 2:40 AM >>> >Dear all >On the current discussion about terms & names: > >(1) --------------------- >I have had the job of teaching our basic Software Engineering course for >some years now. The distinction made by the software engineering (and I >believe more broadly systems engineering) community between Verification >and Validation is quite explicit: > >Verification: > "Are we building the product right?" > > The software should conform to its specification. > >Validation: > "Are we building the right product?" > > The software should do what the user really requires. > >(see e.g. "Software Engineering", Ian Sommerville, 6th edition, Chapter 19) >So verification is *in principle* automatable, being about the equivalence >between one formal system (a spec) and another (a software system). >Validation is *in principle* non-automatable, being about the >correspondence between human requirements and a formal system. > >This is clearly related to, but not the same as, the distinction being made >in other engineering disciplines as e.g. quoted by Ray Moore in his >original posting: >>Evidently "validation" is widely used to refer to agreement with physical >>effects, experimental results, etc. > >I do not think we should get too worried about "right" usage of these >words, seeing that there are various communities out there that use them in >subtly different ways. > >(2) --------------------- >I am perfectly happy with the name "Reliable Computing". I think "Interval >Arithmetic" and "Interval Computing" are too narrow for the reasons Baker >has just given, namely you don't need intervals to get, ermm, validated >results. > >Example: Years ago I refereed a joint paper by two great men, Jim Wilkinson >and Frank Olver, on an algorithm and its implementation, for solving a >(dense) linear system Ax=b with rigorous bounds on the error. This was in >the days when double precision was far slower than single, and before >IEEE754 I think. They just used the Wilkinson model > x OP y = (1 + e) ( x op y), |e| <= u (*) > >where op is an exact arithmetic operation, OP is as done on the machine, u >is the roundoff unit. (I think they even put in an extra term to handle >underflow.) So, the scheme was to do the main computation in double >precision, and simultaneously in single precision perform a running >rigorous error bound of each operation (*), using an inflation of each >absolute-value bound by a factor (1+u1) where u1 is the S.P. roundoff unit, >so as to account for errors in the S.P. computation. You thus did >Wilkinson's backward error analysis but with far sharper bounds, which in >theory would be asymptotically optimal as u -> 0. > >So, totally "validated" but with no interval arithmetic! > >Wilkinson wrote me to the effect that this was Olver's baby, he found it >rather boring and he could have done it on the pilot ACE in 1948 if he had >really wanted to. He was much more interested in error analysis for giving >insight rather than rigorous bounds. But times and needs change. > >--------------------- > >John Pryce > >Dr John D Pryce >Lecturer in Mathematical Software Engineering >Computer Information Systems Engineering Dept >Cranfield University, RMCS Shrivenham >Swindon SN6 8LA, UK >Tel +44 (0)1793-785683 direct, > +44 (0)1793-785931 secretaries, > +44 (0)1793-785366 fax > > > >-- >This message has been scanned for viruses and >dangerous content by the Cranfield MailScanner, and is >believed to be clean. -- best, steve Dr. D. E. Stevenson Director, Institute for Modeling and Simulation Applications Clemson University Clemson,SC 29634-0974 From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Aug 11 18:36:57 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7BNauB3020526 for ; Thu, 11 Aug 2005 18:36:57 -0500 (CDT) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j7BNaunr020525 for reliable_computing-outgoing; Thu, 11 Aug 2005 18:36:56 -0500 (CDT) Received: from itdsrvmail01.utep.edu (itdsrvmail01.utep.edu [129.108.0.82]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7BNahDW020519 for ; Thu, 11 Aug 2005 18:36:53 -0500 (CDT) X-MimeOLE: Produced By Microsoft Exchange V6.5.7226.0 Content-class: urn:content-classes:message MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----_=_NextPart_001_01C59ECD.821E23DE" Subject: FW: Interval arithmetic library in BOOST Date: Thu, 11 Aug 2005 17:34:09 -0600 Message-ID: <77B4C8824930004AAC10E1B01576254A83949F [at] itdsrvmail01 [dot] utep.edu> X-MS-Has-Attach: X-MS-TNEF-Correlator: Thread-Topic: Interval arithmetic library in BOOST Thread-Index: AcWed7rbNd0yMI+HThOCqyXy96BFHQAVXEH7 From: "Kreinovich, Vladik" To: Cc: Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. ------_=_NextPart_001_01C59ECD.821E23DE Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Dear Friends,=20 =20 I have just learned from Sergey Shary an imporratnt info:=20 =20 ... there is an interval C++ library implemented within the popular BOOST project http://www.boost.org. Look at "Libraries", then "Math and numerics", then "Intervals", or just http://www.boost.org/libs/numeric/interval/doc/interval.htm It is one of the most referenced software project among C++ community (an analogue of NETLIB in a sense). Sergey P. Shary Many thanks to Sergey for poiinting out!=20 ------_=_NextPart_001_01C59ECD.821E23DE Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable =0A= =0A= =0A= =0A= =0A= =0A= Interval arithmetic library in BOOST =0A= =0A= =0A=

=0A=

Dear Friends, =

=0A=

I have just learned from = Sergey Shary an =0A= imporratnt info:

=0A=

...

=0A=

there is an interval C++ = library
implemented within =0A= the popular BOOST project http://www.boost.org.
Look at = "Libraries", =0A= then "Math and numerics", then "Intervals",

or =0A= just

http= ://www.boost.org/libs/numeric/interval/doc/interval.htm

It =0A= is one of the most referenced software project among C++ = community
(an =0A= analogue of NETLIB in a sense).

Sergey P. = Shary

Many =0A= thanks to Sergey for poiinting out!

=0A= =0A= =0A= ------_=_NextPart_001_01C59ECD.821E23DE-- From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Aug 12 08:18:42 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7CDIge0021810 for ; Fri, 12 Aug 2005 08:18:42 -0500 (CDT) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j7CDIgaS021809 for reliable_computing-outgoing; Fri, 12 Aug 2005 08:18:42 -0500 (CDT) Received: from zmit1.ippt.gov.pl (zmit1.ippt.gov.pl [148.81.53.8]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7CDIWbc021805 for ; Fri, 12 Aug 2005 08:18:38 -0500 (CDT) Received: (from zkulpa@localhost) by zmit1.ippt.gov.pl (8.8.5/8.7.3-zmit) id PAA09564; Fri, 12 Aug 2005 15:11:41 +0200 (MET DST) Date: Fri, 12 Aug 2005 15:11:41 +0200 (MET DST) From: Zenon Kulpa Message-Id: <200508121311.PAA09564 [at] zmit1 [dot] ippt.gov.pl> To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu Subject: Tolerable/controllable solution applications Cc: zkulpa [at] ippt [dot] gov.pl Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Intervalers, I am looking for some simple examples of practical problems involving control (controllable) and tolerance (tolerable) solution sets of interval linear systems of equations. I would greatly appreciate obtaining references to appropriate papers, or possibly descriptions of the examples. -- Zenon Kulpa From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Aug 12 09:40:45 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7CEeiIg021960 for ; Fri, 12 Aug 2005 09:40:45 -0500 (CDT) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j7CEeipR021959 for reliable_computing-outgoing; Fri, 12 Aug 2005 09:40:44 -0500 (CDT) Received: from itdsrvmail01.utep.edu (itdsrvmail01.utep.edu [129.108.0.82]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7CEeUbt021955 for ; Fri, 12 Aug 2005 09:40:41 -0500 (CDT) X-MimeOLE: Produced By Microsoft Exchange V6.5.7226.0 Content-class: urn:content-classes:message MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----_=_NextPart_001_01C59F4B.C6E02ACA" Subject: interval-related software Date: Fri, 12 Aug 2005 08:40:25 -0600 Message-ID: <77B4C8824930004AAC10E1B01576254A8394B4 [at] itdsrvmail01 [dot] utep.edu> X-MS-Has-Attach: X-MS-TNEF-Correlator: Thread-Topic: interval-related software Thread-Index: AcWfS8bbvNo+YVEUQRmXno82UOCXNQ== From: "Kreinovich, Vladik" To: Cc: Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. ------_=_NextPart_001_01C59F4B.C6E02ACA Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Dear Friends, This is FYI, tow new software links have been added to the = interval website.=20 =20 From: Stefan Ratschan [mailto:stefan.ratschan@mpi-sb.mpg.de] ... =20 * Rsolver: solves quantified inequality constraints (http://rsolver.sourceforge.net) * smathlib: a library of C routines for interval arithmetic and constraint narrowing http://interval.sourceforge.net/interval/prolog/clip/clip/smath/README.ht= ml Thanks, Stefan Ratschan ------_=_NextPart_001_01C59F4B.C6E02ACA Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable =0A=

Dear Friends, This is FYI, = tow new =0A= software links have been added to the interval website. =0A=

=0A=

From: Stefan Ratschan =0A= [mailto:stefan.ratschan@mpi-sb.mpg.de]

=0A=

...

=0A=

* =0A= Rsolver: solves quantified inequality constraints
(http://rsolver.sourceforge.net)
* smathlib: a library of C routines for = interval =0A= arithmetic and
constraint narrowing
http://interval.sourceforge.net/interval/prolog/clip/clip/smath/RE= ADME.html

Thanks,

Stefan =0A= Ratschan

------_=_NextPart_001_01C59F4B.C6E02ACA-- From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Aug 13 15:25:06 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7DKP6Zu027030 for ; Sat, 13 Aug 2005 15:25:06 -0500 (CDT) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j7DKP5xt027029 for reliable_computing-outgoing; Sat, 13 Aug 2005 15:25:05 -0500 (CDT) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7DKP3ar027025 for ; Sat, 13 Aug 2005 15:25:03 -0500 (CDT) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j7DKP2Bi027024 for reliable_computing [at] interval [dot] louisiana.edu; Sat, 13 Aug 2005 15:25:02 -0500 (CDT) Received: from zmit1.ippt.gov.pl (zmit1.ippt.gov.pl [148.81.53.8]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7CGYMsS022156 for ; Fri, 12 Aug 2005 11:34:28 -0500 (CDT) Received: (from zkulpa@localhost) by zmit1.ippt.gov.pl (8.8.5/8.7.3-zmit) id SAA09739 for reliable_computing [at] interval [dot] louisiana.edu; Fri, 12 Aug 2005 18:27:38 +0200 (MET DST) Date: Fri, 12 Aug 2005 18:27:38 +0200 (MET DST) From: Zenon Kulpa Message-Id: <200508121627.SAA09739 [at] zmit1 [dot] ippt.gov.pl> To: reliable_computing [at] interval [dot] louisiana.edu Subject: The other interval list Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk What happened to thee other interval list? Using the address produces the message: 550 interval [at] cs [dot] utep.edu... User unknown Have I possibly missed the change of address? -- Zenon Kulpa From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Aug 13 17:13:22 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7DMDMxH027225 for ; Sat, 13 Aug 2005 17:13:22 -0500 (CDT) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j7DMDMDa027224 for reliable_computing-outgoing; Sat, 13 Aug 2005 17:13:22 -0500 (CDT) Received: from itdsrvmail01.utep.edu (itdsrvmail01.utep.edu [129.108.0.82]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7DMDDjD027219 for ; Sat, 13 Aug 2005 17:13:18 -0500 (CDT) X-MimeOLE: Produced By Microsoft Exchange V6.5.7226.0 Content-class: urn:content-classes:message MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----_=_NextPart_001_01C5A054.2F745C1A" Subject: FW: mailing list on intervals in knowledge representation has been relocated Date: Sat, 13 Aug 2005 16:12:48 -0600 Message-ID: <77B4C8824930004AAC10E1B01576254A8394DA [at] itdsrvmail01 [dot] utep.edu> X-MS-Has-Attach: X-MS-TNEF-Correlator: Thread-Topic: mailing list on intervals in knowledge representation has been relocated Thread-Index: AcWgU85h4fVpQhvhQG22mqiT/xcglAAAD037AAAGCS8= From: "Kreinovich, Vladik" To: Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. ------_=_NextPart_001_01C5A054.2F745C1A Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable =20 Dear Friends, My apologies for the incovenience, our cs.utep.edu mailing = server is down, so the interval in knowledge representation mailing list = interval [at] cs [dot] utep.edu has been relocated to a different server. =20 To send a message to this mailing list please type in = interval [at] listserv [dot] utep.edu =20 The web page for users of the mailing list is:=20 http://listserv.utep.edu/mailman/listinfo/interval=20 Vladik =20 ------_=_NextPart_001_01C5A054.2F745C1A Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable =0A= =0A= =0A=

=0A=

Dear Friends, My = apologies for the =0A= incovenience, our cs.utep.edu mailing server is down, so the interval in =0A= knowledge representation mailing list interval [at] cs [dot] utep.edu has been = relocated =0A= to a different server.

=0A=

To send a message to this mailing list = please type =0A= in interval [at] listserv [dot] utep.edu=

=0A=

The web page for users = of the mailing =0A= list is:

=0A=

http://listserv.utep.edu/mailman/listinfo/interval

=0A=

Vladik

=0A=

------_=_NextPart_001_01C5A054.2F745C1A-- From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Aug 16 05:23:30 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7GANUei004381 for ; Tue, 16 Aug 2005 05:23:30 -0500 (CDT) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j7GANT30004380 for reliable_computing-outgoing; Tue, 16 Aug 2005 05:23:29 -0500 (CDT) Received: from wminf0.math.uni-wuppertal.de (wminf0.math.uni-wuppertal.de [132.195.94.17]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7GANK1p004376 for ; Tue, 16 Aug 2005 05:23:26 -0500 (CDT) Received: from imap.math.uni-wuppertal.de (imap.math.uni-wuppertal.de [132.195.94.36]) by wminf0.math.uni-wuppertal.de (8.9.3+Sun/8.9.3) with ESMTP id MAA08930 for ; Tue, 16 Aug 2005 12:23:14 +0200 (MEST) Received: from math.uni-wuppertal.de (wmai03.math.uni-wuppertal.de [132.195.95.3]) (using TLSv1 with cipher RC4-MD5 (128/128 bits)) (Client did not present a certificate) by imap.math.uni-wuppertal.de (Postfix) with ESMTP id 2E7096550C for ; Tue, 16 Aug 2005 12:23:14 +0200 (CEST) Message-ID: <4301BE92.301 [at] math [dot] uni-wuppertal.de> Date: Tue, 16 Aug 2005 12:23:14 +0200 From: Bruno Lang User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.4.3) Gecko/20050104 X-Accept-Language: en-us, en MIME-Version: 1.0 To: reliable_computing [at] interval [dot] louisiana.edu Subject: CFP: ECMI Newsletter, Issue on result-verifying computations X-Enigmail-Version: 0.76.8.0 X-Enigmail-Supports: pgp-inline, pgp-mime Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear fellow intervalers, Andreas Frommer and I will be guest editors for one of the next issues of the ECMI Newsletter, a journal of the European Consortium for Mathematics in Industry; see http://www.ecmi-indmath.org This issue is intended as a vehicle for promoting ideas from result-verifying computing (interval and related methods) to engineers working in industry. Given the format and audience of the journal, each contribution should be kind of an "appetizer", i.e., it should - be short (2 pp max) - describe an application of result-verifying computing, either in cooperation with industry or with obvious impact to industry, and - keep technical details at a minimum and instead give pointers. The contributions will be preceded by a short introduction into interval (and related) methods. Note that the papers will NOT undergo a full peer review process. If you are interested in contributing to this issue, please send us a short (plain text) message describing the application and how result-verifying methods came into play. Based on these descriptions we will select the contributions and contact you for the submission of the full length (2pp) version. With your help, we hope to collect at least half a dozen applications highlighting different aspects of result-verifying methods. Andreas Frommer (frommer [at] math [dot] uni-wuppertal.de) and Bruno Lang (lang [at] math [dot] uni-wuppertal.de) From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Aug 17 07:30:37 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7HCUaVR007006 for ; Wed, 17 Aug 2005 07:30:36 -0500 (CDT) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j7HCUaBM007005 for reliable_computing-outgoing; Wed, 17 Aug 2005 07:30:36 -0500 (CDT) Received: from ms-smtp-02-eri0.ohiordc.rr.com (ms-smtp-02-smtplb.ohiordc.rr.com [65.24.5.136]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7HCURMb007001 for ; Wed, 17 Aug 2005 07:30:33 -0500 (CDT) Received: from Moore (cpe-204-210-226-96.columbus.res.rr.com [204.210.226.96]) by ms-smtp-02-eri0.ohiordc.rr.com (8.12.10/8.12.7) with SMTP id j7HCUOXX000227 for ; Wed, 17 Aug 2005 08:30:25 -0400 (EDT) Message-ID: <002601c5a327$7ef40320$0202a8c0@Moore> From: "Ray Moore" To: "reliable computing" Subject: Eigenvalue enclosures Date: Wed, 17 Aug 2005 08:30:47 -0400 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0023_01C5A305.F7A92AB0" 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-Virus-Scanned: Symantec AntiVirus Scan Engine Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. ------=_NextPart_000_0023_01C5A305.F7A92AB0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Dear Colleagues, I have been asked the following question, and do not know of such a = program. Is there one? Is it available? "Do you know about any program which can make inclusion of the = eigenvalues for a positive definite matrix say with 1000 or more = unknowns for example of the finite element type? If so do you have some = experience with that?" best regards, Ray Moore ------=_NextPart_000_0023_01C5A305.F7A92AB0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Dear Colleagues,

I have been asked the following = question, and do=20 not know of such a program. Is there one? Is it available?

"Do you know=20 about any program which can make inclusion of the eigenvalues for = a=20 positive definite matrix say with 1000 or more unknowns for = example of the=20 finite element type? If so do you have some experience with=20 that?"

best=20 regards,

Ray=20 Moore

------=_NextPart_000_0023_01C5A305.F7A92AB0-- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Aug 17 12:44:52 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7HHiqtB007439 for ; Wed, 17 Aug 2005 12:44:52 -0500 (CDT) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.4/Submit) id j7HHiqfk007438 for reliable_computing-outgoing; Wed, 17 Aug 2005 12:44:52 -0500 (CDT) Received: from signals.gtrep.gatech.edu (signals.gtrep.gatech.edu [168.20.172.14]) by interval.louisiana.edu (8.13.1/8.13.4/ull-interval-math-majordomo-1.5) with ESMTP id j7HHierZ007433 for ; Wed, 17 Aug 2005 12:44:49 -0500 (CDT) Received: from rmuhannalptp (rmuhanna-lptp.gtrep.gatech.edu [10.50.20.152]) by signals.gtrep.gatech.edu (8.12.8/8.12.8) with SMTP id j7HHiS6f028415; Wed, 17 Aug 2005 13:44:28 -0400 Message-ID: <004801c5a353$4d228c50$9814320a@rmuhannalptp> From: "Rafi Muhanna" To: "Ray Moore" , "reliable computing" References: <002601c5a327$7ef40320$0202a8c0@Moore> Subject: Re: Eigenvalue enclosures Date: Wed, 17 Aug 2005 13:44:21 -0400 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0045_01C5A331.C5B3B120" 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-GTSAV-MailScanner-Information: Please contact the ISP for more information X-GTSAV-MailScanner: Found to be clean X-MailScanner-From: rafi.muhanna [at] gtrep [dot] gatech.edu Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. ------=_NextPart_000_0045_01C5A331.C5B3B120 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Dear Prof. Moore, The following two papers might have answers to your questions: 1. Modares, Mehdi and Mullen, Robert L., 2004. " Free Vibration of = Structures with Interval Uncertainty ". 9th ASCE Specialty Conference on = Probabilistic Mechanics and Structural Reliability, New Mexico, July = 26-28, 2004. 2. Modares, M., Mullen, R., Bellini, P., and Muhanna, R., "Buckling = Analysis of Structures with Interval Parameters," the 2005 SAE World = Congress, Reliability and Robust Design in Automotive Engineering, = Detroit, Michigan, April 11-14, 2005. Best regards, Rafi Muhanna ----- Original Message -----=20 From: Ray Moore=20 To: reliable computing=20 Sent: Wednesday, August 17, 2005 8:30 AM Subject: Eigenvalue enclosures Dear Colleagues, I have been asked the following question, and do not know of such a = program. Is there one? Is it available? "Do you know about any program which can make inclusion of the = eigenvalues for a positive definite matrix say with 1000 or more = unknowns for example of the finite element type? If so do you have some = experience with that?" best regards, Ray Moore ------=_NextPart_000_0045_01C5A331.C5B3B120 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

Dear Prof. Moore,

The following two papers might have = answers=20 to your questions:

1. Modares, Mehdi = and=20 Mullen, Robert L., 2004. =93 Free Vibration of Structures with Interval=20 Uncertainty =94. 9^th ASCE Specialty Conference on = Probabilistic=20 Mechanics and Structural Reliability, New Mexico, July 26-28, 2004.

2. = Modares, M., Mullen, R., Bellini, P., = and Muhanna,=20 R., =93Buckling Analysis = of Structures=20 with Interval Parameters,=94 the 2005=20 SAE World Congress, Reliability and Robust Design in Automotive = Engineering,=20 Detroit, Michigan, April 11-14, 2005.

Best regards,

Rafi Muhanna

----- Original Message = -----=20

From:=20 Ray=20 Moore