Subject: Reliable Computing, Vol.11, issue 3, 2005
Date: Tue, 8 Feb 2005 22:30:42 +0300
MIME-Version: 1.0
Content-Type: multipart/alternative;
boundary="----=_NextPart_000_00A6_01C50E2D.D2C1F190"
X-Priority: 3
X-MSMail-Priority: Normal
X-Mailer: Microsoft Outlook Express 6.00.2800.1106
X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106
X-Spam: Not detected
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
This is a multi-part message in MIME format.
------=_NextPart_000_00A6_01C50E2D.D2C1F190
Content-Type: text/plain;
charset="koi8-r"
Content-Transfer-Encoding: quoted-printable
Reliable Computing
Volume 11, issue 3, 2005
Mathematical Research
Enclosing Solutions of Singular Interval Systems Iteratively
Goetz Alefeld, Guenter Mayer
165-190
Fast Inclusion of Interval Matrix Multiplication=20
Takeshi Ogita, Shin'ichi Oishi
191-205
Exact Bounds on Finite Populations of Interval Data
Scott Ferson, Lev Ginzburg, Vladik Kreinovich, Luc Longpre, Monica =
Aviles
207-233
Tolerances in Geometric Constraint Problems
Johannes Wallner, Hans-Peter Schroecker, Shi-Min Hu
235-251
------=_NextPart_000_00A6_01C50E2D.D2C1F190
Content-Type: text/html;
charset="koi8-r"
Content-Transfer-Encoding: quoted-printable
&nbs=
p; =20
Reliable=20
Computing

=
=20
Volume 11, issue 3, 2005

&nbs=
p;=20
Mathematical Research

Enclosing Solutions of Singular =
Interval Systems=20
Iteratively

Goetz Alefeld, Guenter Mayer

165-190

Fast Inclusion of Interval Matrix =
Multiplication=20

Takeshi Ogita, Shin'ichi Oishi

191-205

Exact Bounds on Finite Populations of =
Interval=20
Data

Scott Ferson, Lev Ginzburg, Vladik Kreinovich, Luc Longpre, =
Monica=20
Aviles

207-233

Tolerances in Geometric Constraint=20
Problems

Johannes Wallner, Hans-Peter Schroecker, Shi-Min=20
Hu

235-251

------=_NextPart_000_00A6_01C50E2D.D2C1F190--
From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Feb 15 23:27:50 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1G5RoNx028120
for ; Tue, 15 Feb 2005 23:27:50 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1G5RoI9028119
for reliable_computing-outgoing; Tue, 15 Feb 2005 23:27:50 -0600 (CST)
Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1G5RfVh028114
for ; Tue, 15 Feb 2005 23:27:47 -0600 (CST)
Received: from aragorn (aragorn [129.108.5.35])
by cs.utep.edu (8.11.7/8.11.7) with SMTP id j1G5RBt19348;
Tue, 15 Feb 2005 22:27:11 -0700 (MST)
Message-Id: <200502160527.j1G5RBt19348 [at] cs [dot] utep.edu>
Date: Tue, 15 Feb 2005 22:27:11 -0700 (MST)
From: Vladik Kreinovich
Reply-To: Vladik Kreinovich
Subject: a book of potential interest to interval researchers
To: reliable_computing [at] interval [dot] louisiana.edu
Cc: chleb [at] math [dot] cas.cz
MIME-Version: 1.0
Content-Type: TEXT/plain; charset=us-ascii
Content-MD5: eUVL2bxhxe4PovM/tDhigQ==
X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
Forwarding, from NA Digest
******************************************
From: Jan Chleboun
Date: Wed, 9 Feb 2005 12:09:50 +0100 (CET)
Subject: New Book on Uncertain Input Data
Uncertain Input Data Problems and the Worst Scenario Method
by Ivan Hlavacek, Jan Chleboun, and Ivo Babuska;
North-Holland Series in Applied Mathematics and Mechanics, Volume 46,
Elsevier, Amsterdam, December 2004.
Hardback, xxvi+458 pages, ISBN: 0-444-51435-X
This book deals with the impact of uncertainty in input data on the
outputs of mathematical models. Uncertain inputs as scalars, tensors,
functions, or domain boundaries are considered. In practical terms,
material parameters or constitutive laws, for instance, are uncertain, and
quantities as local temperature, local mechanical stress, or local
displacement are monitored. The goal of the worst scenario method is to
extremize the quantity over the set of uncertain input data.
A general mathematical scheme of the worst scenario method, including
approximation by finite element methods, is presented, and then applied to
various state problems modeled by differential equations or variational
inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling,
plate buckling, contact problems in elasticity and thermoelasticity with
and without friction, and various models of plastic deformation, to list
some of the topics. Dozens of examples, figures, and tables are included.
More details can be found at
http://books.elsevier.com/elsevier/?isbn=044451435X
Jan Chleboun
Mathematical Institute
Academy of Sciences
Zitna 25 ( TeX: \v{Z}itn\'a )
115 67 Prague 1
Czech Republic
e-mail: chleb [at] math [dot] cas.cz
From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 06:38:02 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GCc2J9029074
for ; Wed, 16 Feb 2005 06:38:02 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GCc2EC029073
for reliable_computing-outgoing; Wed, 16 Feb 2005 06:38:02 -0600 (CST)
Received: from ms-smtp-03-eri0.ohiordc.rr.com (ms-smtp-03-smtplb.ohiordc.rr.com [65.24.5.137])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GCbrdY029069
for ; Wed, 16 Feb 2005 06:37:59 -0600 (CST)
Received: from Moore (wor226111.columbus.rr.com [204.210.226.111])
by ms-smtp-03-eri0.ohiordc.rr.com (8.12.10/8.12.7) with SMTP id j1GC0jwZ018590;
Wed, 16 Feb 2005 07:00:45 -0500 (EST)
Message-ID: <000701c5141f$364f8550$1702a8c0@Moore>
From: "Ray Moore"
To: "Vladik Kreinovich" ,
Cc:
References: <200502160527.j1G5RBt19348 [at] cs [dot] utep.edu>
Subject: Re: a book of potential interest to interval researchers
Date: Wed, 16 Feb 2005 07:00:51 -0500
MIME-Version: 1.0
Content-Type: text/plain;
format=flowed;
charset="iso-8859-1";
reply-type=original
Content-Transfer-Encoding: 7bit
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
It seems odd to me that there is no mention of interval computation in the
book.
Ray Moore
----- Original Message -----
From: "Vladik Kreinovich"
To:
Cc:
Sent: Wednesday, February 16, 2005 12:27 AM
Subject: a book of potential interest to interval researchers
> Forwarding, from NA Digest
> ******************************************
> From: Jan Chleboun
> Date: Wed, 9 Feb 2005 12:09:50 +0100 (CET)
> Subject: New Book on Uncertain Input Data
>
> Uncertain Input Data Problems and the Worst Scenario Method
> by Ivan Hlavacek, Jan Chleboun, and Ivo Babuska;
> North-Holland Series in Applied Mathematics and Mechanics, Volume 46,
> Elsevier, Amsterdam, December 2004.
> Hardback, xxvi+458 pages, ISBN: 0-444-51435-X
>
> This book deals with the impact of uncertainty in input data on the
> outputs of mathematical models. Uncertain inputs as scalars, tensors,
> functions, or domain boundaries are considered. In practical terms,
> material parameters or constitutive laws, for instance, are uncertain, and
> quantities as local temperature, local mechanical stress, or local
> displacement are monitored. The goal of the worst scenario method is to
> extremize the quantity over the set of uncertain input data.
>
> A general mathematical scheme of the worst scenario method, including
> approximation by finite element methods, is presented, and then applied to
> various state problems modeled by differential equations or variational
> inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling,
> plate buckling, contact problems in elasticity and thermoelasticity with
> and without friction, and various models of plastic deformation, to list
> some of the topics. Dozens of examples, figures, and tables are included.
>
> More details can be found at
> http://books.elsevier.com/elsevier/?isbn=044451435X
>
> Jan Chleboun
> Mathematical Institute
> Academy of Sciences
> Zitna 25 ( TeX: \v{Z}itn\'a )
> 115 67 Prague 1
> Czech Republic
> e-mail: chleb [at] math [dot] cas.cz
>
>
From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 09:26:51 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GFQpoe029452
for ; Wed, 16 Feb 2005 09:26:51 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GFQo3g029451
for reliable_computing-outgoing; Wed, 16 Feb 2005 09:26:50 -0600 (CST)
Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GFQgju029447
for ; Wed, 16 Feb 2005 09:26:47 -0600 (CST)
Received: from aragorn (aragorn [129.108.5.35])
by cs.utep.edu (8.11.7/8.11.7) with SMTP id j1GFQao21752;
Wed, 16 Feb 2005 08:26:36 -0700 (MST)
Message-Id: <200502161526.j1GFQao21752 [at] cs [dot] utep.edu>
Date: Wed, 16 Feb 2005 08:26:36 -0700 (MST)
From: Vladik Kreinovich
Reply-To: Vladik Kreinovich
Subject: Re: a book of potential interest to interval researchers
To: vladik [at] cs [dot] utep.edu, reliable_computing [at] interval [dot] louisiana.edu,
rmoore17 [at] columbus [dot] rr.com
Cc: chleb [at] math [dot] cas.cz
MIME-Version: 1.0
Content-Type: TEXT/plain; charset=us-ascii
Content-MD5: XTf0GpWmKSCp5/BA/vzTOg==
X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
Dear Ray,
I agree with you 100%.
There may be a mention of intervals inside, but it is unusul that these
techniques are not mentioned in the general description - while the topic seems
to be taylor-made for the interval techniques.
That is why I forwarded this information to the interval mailing list: that
this is an overview of the problems where interval will probably help and are
not under-used.
As you may remember from some of my previous email, I am currently starting to
work together with Dr. Pavel Solin, one of the former co-workers of Dr. Babuska
(he invited Babuska to El Paso last year). From my experience of working with
Dr. Solin, he is enthusaistic about all possible techniques, he is just not
that familiar with interval techniques and their capabilities. I think this is
one more opportunity for us to teach our techniques to a new set of folks, and
by collaborating with them convince them that interval techniques should
definitely be a part of their toolbox.
In my experience of working with engineers and applied mathematicians,
sometimes the problem is that they do not appreciate th eneed for validated
guaranteed worts-case estimates.
This book is an example of an area where the problem is well-understood and
since this problem is exactly what our interval techniques are good at solving,
there is a great potential of using these techniques.
This is one of the reasons why I am so enthusiastic about this book and
potential for usese of interval techniques.
Vladik
> From: "Ray Moore"
> To: "Vladik Kreinovich" ,
> Cc:
> Subject: Re: a book of potential interest to interval researchers
> Date: Wed, 16 Feb 2005 07:00:51 -0500
> MIME-Version: 1.0
> Content-Transfer-Encoding: 7bit
> X-Priority: 3
> X-MSMail-Priority: Normal
> X-MIMEOLE: Produced By Microsoft MimeOLE V6.00.2900.2180
> X-Virus-Scanned: Symantec AntiVirus Scan Engine
>
> It seems odd to me that there is no mention of interval computation in the
> book.
>
> Ray Moore
>
> ----- Original Message -----
> From: "Vladik Kreinovich"
> To:
> Cc:
> Sent: Wednesday, February 16, 2005 12:27 AM
> Subject: a book of potential interest to interval researchers
>
>
> > Forwarding, from NA Digest
> > ******************************************
> > From: Jan Chleboun
> > Date: Wed, 9 Feb 2005 12:09:50 +0100 (CET)
> > Subject: New Book on Uncertain Input Data
> >
> > Uncertain Input Data Problems and the Worst Scenario Method
> > by Ivan Hlavacek, Jan Chleboun, and Ivo Babuska;
> > North-Holland Series in Applied Mathematics and Mechanics, Volume 46,
> > Elsevier, Amsterdam, December 2004.
> > Hardback, xxvi+458 pages, ISBN: 0-444-51435-X
> >
> > This book deals with the impact of uncertainty in input data on the
> > outputs of mathematical models. Uncertain inputs as scalars, tensors,
> > functions, or domain boundaries are considered. In practical terms,
> > material parameters or constitutive laws, for instance, are uncertain, and
> > quantities as local temperature, local mechanical stress, or local
> > displacement are monitored. The goal of the worst scenario method is to
> > extremize the quantity over the set of uncertain input data.
> >
> > A general mathematical scheme of the worst scenario method, including
> > approximation by finite element methods, is presented, and then applied to
> > various state problems modeled by differential equations or variational
> > inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling,
> > plate buckling, contact problems in elasticity and thermoelasticity with
> > and without friction, and various models of plastic deformation, to list
> > some of the topics. Dozens of examples, figures, and tables are included.
> >
> > More details can be found at
> > http://books.elsevier.com/elsevier/?isbn=044451435X
> >
> > Jan Chleboun
> > Mathematical Institute
> > Academy of Sciences
> > Zitna 25 ( TeX: \v{Z}itn\'a )
> > 115 67 Prague 1
> > Czech Republic
> > e-mail: chleb [at] math [dot] cas.cz
> >
> >
From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 10:24:41 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GGOfOW029595
for ; Wed, 16 Feb 2005 10:24:41 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GGOfJb029594
for reliable_computing-outgoing; Wed, 16 Feb 2005 10:24:41 -0600 (CST)
Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GGOWSv029590
for ; Wed, 16 Feb 2005 10:24:38 -0600 (CST)
Received: from aragorn (aragorn [129.108.5.35])
by cs.utep.edu (8.11.7/8.11.7) with SMTP id j1GGORf22170;
Wed, 16 Feb 2005 09:24:27 -0700 (MST)
Message-Id: <200502161624.j1GGORf22170 [at] cs [dot] utep.edu>
Date: Wed, 16 Feb 2005 09:24:27 -0700 (MST)
From: Vladik Kreinovich
Reply-To: Vladik Kreinovich
Subject: a course of potential interest to interval researchers
To: reliable_computing [at] interval [dot] louisiana.edu
Cc: mceberio [at] utep [dot] edu
MIME-Version: 1.0
Content-Type: TEXT/plain; charset=us-ascii
Content-MD5: +AhxrwbWrsBRJfWo9oDWOA==
X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
Dear Friends,
As many of you know, I have recently joined a group of people interested in
extended interval techniques to the situations when, in addition to guaranteed
(interval) bounds, we also have some partial information about the probability
of different values within the corresponding intervals.
This activivity was pioneered by Ray Moore himself in his 1980s papers, Dan
Berleant has a website (easily acceissble from the interval webpage) on
probabilities and intervals.
For control applications, this activity was done in 1990s by Bob Barmish, the
author of one of the most well-known books on interval-based (robust) control.
>From this viewpoint, the following course may be of interest to many
researchers from our community.
Many thanks to Greg Coxson for brining this to our attention.
------------- Begin Forwarded Message -------------
Date: Wed, 16 Feb 2005 09:19:51 -0500
From: "Coxson, Gregory E"
I wonder if those in the group would be
interested in this that I took off the
Control Theory eLetter.
...
Course on Randomized Algorithms for Analysis and Control of Uncertain
Systems
Lecturer: Roberto Tempo
IEIIT-CNR
Politecnico di Torino, Italy
tempo [at] polito [dot] it
Date: March 14-18, 2005
Place : Dept. Ing. de Sistemas y Automatica
Escuela Superior de Ingenieros, Univ. Sevilla, Spain
Summary
This course concentrates on nonstandard tools for control of uncertain
systems with main emphasis on the interplay of probability and
robustness.
The objective is to combine hard bounds, which are frequently used in
classical robust control, with probabilistic information which is often
neglected in this context. The main advantage is to provide additional
insight to the control engineer. This insight may be very useful in
analyzing and designing complex control systems in the presence of
uncertainty. The interplay of probability and robustness also leads to
innovative concepts such as the probabilistic robustness margin and the
probability degradation function. The algorithms obtained are low
complexity (polynomial-time) and are associated to robustness bounds
which are generally less conservative than the classical ones, obviously
at the expense of a small risk expressed in probability. These
algorithms
are usually called "randomized algorithms."
In the first part of the course, we concentrate on analysis and, in
particular, we address the issue of finite sample size. Subsequently, we
present results for sample generation in various norm-bounded sets of
interest in robust control. These results are based on methods of
statistical analysis and of the theory of random matrices. The
construction of specific randomized algorithms concludes this part of
the
course. In the second part, we study probabilistic robust design of
uncertain systems. We show how this problem can be formulated in the
context of classical optimal control and then we discuss how
randomization
and stochastic gradient methods can be successfully used. We also
consider extensions of this approach to linear parameter-varying
systems. Other topics that will be addressed is the design of randomized
algorithms for model predictive control and for robust fault-tolerant
control.
The course will end with a description of a number of open problems
which
may be important to consider in the near future.
The course is focused on the exposition of the theoretical developments
as well as on simulations showing the efficacy of these techniques.
Main list of topics
- Preliminaries and Motivations for a Probabilistic Approach
- Uncertain Systems
- The Interplay of Probability and Robustness
- Randomized Algorithms
- Sample Size Bounds and Statistical Learning Theory
- Sample Generation Theory
- Probabilistic Robust Design with Linear Quadratic Regulators
- Probabilistic Design for Linear Parameter-Varying Systems
- Randomized Algorithms for Model Predictive Control
- Applications (robustness of high-speed networks, stability of
quantized
sampled-data systems, performance of flexible structures)
- Discussion of Open Research Problems
The course is funded by the Spanish Ministry of Education and and no
fees will
be charged. The number of places is limited and a first in first served
system
will be used.
Registration: e-mail to eduardo [at] esi [dot] us.es
------------- End Forwarded Message -------------
From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 10:49:14 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GGnDse029756
for ; Wed, 16 Feb 2005 10:49:13 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GGnDei029755
for reliable_computing-outgoing; Wed, 16 Feb 2005 10:49:13 -0600 (CST)
Received: from mail-mta.sunlabs.com (dyn50.sunlabs.com [204.153.12.50])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GGn3ll029750
for ; Wed, 16 Feb 2005 10:49:09 -0600 (CST)
Received: from mail.sunlabs.com ([152.70.2.186]) by mail-mta.sfvic.sunlabs.com
(Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004))
with ESMTP id <0IC00063UK15PV00@mail-mta.sfvic.sunlabs.com> for
reliable_computing [at] interval [dot] louisiana.edu; Wed,
16 Feb 2005 08:48:41 -0800 (PST)
Received: from [129.146.72.246] by mail.sunlabs.com
(Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004))
with ESMTPSA id <0IC000BK0K14MH10 [at] mail [dot] sunlabs.com> for
reliable_computing [at] interval [dot] louisiana.edu; Wed,
16 Feb 2005 08:48:41 -0800 (PST)
Date: Wed, 16 Feb 2005 08:48:44 -0800
From: "G. William Walster"
Subject: Re: a book of potential interest to interval researchers
In-reply-to: <000701c5141f$364f8550$1702a8c0@Moore>
To: Ray Moore
Cc: Vladik Kreinovich ,
reliable_computing [at] interval [dot] louisiana.edu, chleb [at] math [dot] cas.cz
Reply-to: Bill.Walster [at] sun [dot] com
Message-id: <4213796C.3080008 [at] sun [dot] com>
Organization: Sun Microsystems Laboratories
MIME-version: 1.0
Content-type: text/plain; charset=us-ascii; format=flowed
Content-transfer-encoding: 7BIT
X-Accept-Language: en-us, en
References: <200502160527.j1G5RBt19348 [at] cs [dot] utep.edu>
<000701c5141f$364f8550$1702a8c0@Moore>
User-Agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X Mach-O; en-US; rv:1.7)
Gecko/20040616
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
I agree.
I have ordered it from Amazon. Perhaps the authors don't know
about intervals. Many people still do not.
The encouraging thing is that even point people are starting
to realize the importance of input uncertainty. This can only
be good for us. :)
Cheers,
Bill
P.S. If nothing else, this is a source of good examples for
you to use in your talk. :)
Ray Moore wrote:
> It seems odd to me that there is no mention of interval computation in
> the book.
>
> Ray Moore
>
> ----- Original Message ----- From: "Vladik Kreinovich"
> To:
> Cc:
> Sent: Wednesday, February 16, 2005 12:27 AM
> Subject: a book of potential interest to interval researchers
>
>
>> Forwarding, from NA Digest
>> ******************************************
>> From: Jan Chleboun
>> Date: Wed, 9 Feb 2005 12:09:50 +0100 (CET)
>> Subject: New Book on Uncertain Input Data
>>
>> Uncertain Input Data Problems and the Worst Scenario Method
>> by Ivan Hlavacek, Jan Chleboun, and Ivo Babuska;
>> North-Holland Series in Applied Mathematics and Mechanics, Volume 46,
>> Elsevier, Amsterdam, December 2004.
>> Hardback, xxvi+458 pages, ISBN: 0-444-51435-X
>>
>> This book deals with the impact of uncertainty in input data on the
>> outputs of mathematical models. Uncertain inputs as scalars, tensors,
>> functions, or domain boundaries are considered. In practical terms,
>> material parameters or constitutive laws, for instance, are uncertain,
>> and
>> quantities as local temperature, local mechanical stress, or local
>> displacement are monitored. The goal of the worst scenario method is to
>> extremize the quantity over the set of uncertain input data.
>>
>> A general mathematical scheme of the worst scenario method, including
>> approximation by finite element methods, is presented, and then
>> applied to
>> various state problems modeled by differential equations or variational
>> inequalities: nonlinear heat flow, Timoshenko beam vibration and
>> buckling,
>> plate buckling, contact problems in elasticity and thermoelasticity with
>> and without friction, and various models of plastic deformation, to list
>> some of the topics. Dozens of examples, figures, and tables are included.
>>
>> More details can be found at
>> http://books.elsevier.com/elsevier/?isbn=044451435X
>>
>> Jan Chleboun
>> Mathematical Institute
>> Academy of Sciences
>> Zitna 25 ( TeX: \v{Z}itn\'a )
>> 115 67 Prague 1
>> Czech Republic
>> e-mail: chleb [at] math [dot] cas.cz
>>
>>
>
From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 10:50:14 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GGoDR7029804
for ; Wed, 16 Feb 2005 10:50:13 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GGoDQD029802
for reliable_computing-outgoing; Wed, 16 Feb 2005 10:50:13 -0600 (CST)
Received: from mail-mta.sunlabs.com (dyn50.sunlabs.com [204.153.12.50])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GGo0KV029793
for ; Wed, 16 Feb 2005 10:50:06 -0600 (CST)
Received: from mail.sunlabs.com ([152.70.2.186]) by mail-mta.sfvic.sunlabs.com
(Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004))
with ESMTP id <0IC000644K37PV00@mail-mta.sfvic.sunlabs.com> for
reliable_computing [at] interval [dot] louisiana.edu; Wed,
16 Feb 2005 08:49:55 -0800 (PST)
Received: from [129.146.72.246] by mail.sunlabs.com
(Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004))
with ESMTPSA id <0IC000BK6K36MH10 [at] mail [dot] sunlabs.com> for
reliable_computing [at] interval [dot] louisiana.edu; Wed,
16 Feb 2005 08:49:55 -0800 (PST)
Date: Wed, 16 Feb 2005 08:49:58 -0800
From: "G. William Walster"
Subject: P.S.
In-reply-to: <000701c5141f$364f8550$1702a8c0@Moore>
To: Ray Moore
Cc: Vladik Kreinovich ,
reliable_computing [at] interval [dot] louisiana.edu, chleb [at] math [dot] cas.cz
Reply-to: Bill.Walster [at] sun [dot] com
Message-id: <421379B6.6050504 [at] sun [dot] com>
Organization: Sun Microsystems Laboratories
MIME-version: 1.0
Content-type: text/plain; charset=us-ascii; format=flowed
Content-transfer-encoding: 7BIT
X-Accept-Language: en-us, en
References: <200502160527.j1G5RBt19348 [at] cs [dot] utep.edu>
<000701c5141f$364f8550$1702a8c0@Moore>
User-Agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X Mach-O; en-US; rv:1.7)
Gecko/20040616
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
P.S.
Did you have any comments about the short note I sent
regarding the use of Popper's ideas?
Cheers,
Bill
From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 11:04:39 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GH4dPx029984
for ; Wed, 16 Feb 2005 11:04:39 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GH4cuV029983
for reliable_computing-outgoing; Wed, 16 Feb 2005 11:04:38 -0600 (CST)
Received: from mail-mta.sunlabs.com (dyn50.sunlabs.com [204.153.12.50])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GH4INq029979
for ; Wed, 16 Feb 2005 11:04:28 -0600 (CST)
Received: from mail.sunlabs.com ([152.70.2.186]) by mail-mta.sfvic.sunlabs.com
(Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004))
with ESMTP id <0IC00064NKQTPV00@mail-mta.sfvic.sunlabs.com> for
reliable_computing [at] interval [dot] louisiana.edu; Wed,
16 Feb 2005 09:04:05 -0800 (PST)
Received: from [129.146.72.246] by mail.sunlabs.com
(Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004))
with ESMTPSA id <0IC000BL9KQPMH10 [at] mail [dot] sunlabs.com> for
reliable_computing [at] interval [dot] louisiana.edu; Wed,
16 Feb 2005 09:04:02 -0800 (PST)
Date: Wed, 16 Feb 2005 09:04:05 -0800
From: "G. William Walster"
Subject: Re: P.S.
In-reply-to: <421379B6.6050504 [at] sun [dot] com>
To: Bill.Walster [at] sun [dot] com
Cc: Ray Moore ,
Vladik Kreinovich ,
reliable_computing [at] interval [dot] louisiana.edu, chleb [at] math [dot] cas.cz
Reply-to: Bill.Walster [at] sun [dot] com
Message-id: <42137D05.2040003 [at] sun [dot] com>
Organization: Sun Microsystems Laboratories
MIME-version: 1.0
Content-type: multipart/mixed; boundary="Boundary_(ID_U3KS6C0RmmCtPus/Fz0qAA)"
X-Accept-Language: en-us, en
References: <200502160527.j1G5RBt19348 [at] cs [dot] utep.edu>
<000701c5141f$364f8550$1702a8c0@Moore> <421379B6.6050504 [at] sun [dot] com>
User-Agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X Mach-O; en-US; rv:1.7)
Gecko/20040616
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
This is a multi-part message in MIME format.
--Boundary_(ID_U3KS6C0RmmCtPus/Fz0qAA)
Content-type: text/plain; charset=us-ascii; format=flowed
Content-transfer-encoding: 7BIT
Sorry, everybody, but Ray.
I intended this only for him, for now.
The note I referred to is still a "work in progress".
Nevertheless, I would appreciate any feedback regarding it.
Thanks in advance,
Bill
G. William Walster wrote:
>
> P.S.
>
> Did you have any comments about the short note I sent
> regarding the use of Popper's ideas?
>
> Cheers,
>
> Bill
>
--Boundary_(ID_U3KS6C0RmmCtPus/Fz0qAA)
Content-type: application/pdf; x-mac-type=0; x-mac-creator=0; name=draft03.pdf
Content-transfer-encoding: base64
Content-disposition: inline; filename=draft03.pdf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--Boundary_(ID_U3KS6C0RmmCtPus/Fz0qAA)--
From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 13:20:20 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GJKKD0000314
for ; Wed, 16 Feb 2005 13:20:20 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GJKJjX000313
for reliable_computing-outgoing; Wed, 16 Feb 2005 13:20:19 -0600 (CST)
Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GJKART000309
for ; Wed, 16 Feb 2005 13:20:17 -0600 (CST)
Received: from aragorn (aragorn [129.108.5.35])
by cs.utep.edu (8.11.7/8.11.7) with SMTP id j1GJK5w23518;
Wed, 16 Feb 2005 12:20:05 -0700 (MST)
Message-Id: <200502161920.j1GJK5w23518 [at] cs [dot] utep.edu>
Date: Wed, 16 Feb 2005 12:20:06 -0700 (MST)
From: Vladik Kreinovich
Reply-To: Vladik Kreinovich
Subject: Re: P.S.
To: Bill.Walster [at] sun [dot] com
Cc: reliable_computing [at] interval [dot] louisiana.edu
MIME-Version: 1.0
Content-Type: TEXT/plain; charset=us-ascii
Content-MD5: 7JSJAlWeE8YmoTtPehGxag==
X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
Correction about monotonicity:
If the function is monotonic in each of the variables, you do not need 2^n
computations, only n+3 to find the range: first, you modify the 1st variable to
see if the function if the function is increasing or decreasing over x1; then
you change the 2nd variable only to see whether it is increasing or decreasing
over x2, etc.
After n such calls to f, you know where exactly f attains its maximum and where
it attains its minimum, so you need 2 calls to f to find both upper endpoint
and lower endpoint of the range.
> Date: Wed, 16 Feb 2005 09:04:05 -0800
> From: "G. William Walster"
> Subject: Re: P.S.
> To: Bill.Walster [at] sun [dot] com
> Cc: Ray Moore , Vladik Kreinovich
, reliable_computing [at] interval [dot] louisiana.edu,
chleb [at] math [dot] cas.cz
> MIME-version: 1.0
> X-Accept-Language: en-us, en
> User-Agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X Mach-O; en-US; rv:1.7)
Gecko/20040616
>
>
>
> Sorry, everybody, but Ray.
>
> I intended this only for him, for now.
>
> The note I referred to is still a "work in progress".
>
> Nevertheless, I would appreciate any feedback regarding it.
>
> Thanks in advance,
>
> Bill
>
>
> G. William Walster wrote:
>
> >
> > P.S.
> >
> > Did you have any comments about the short note I sent
> > regarding the use of Popper's ideas?
> >
> > Cheers,
> >
> > Bill
> >
>
------------- End Forwarded Message -------------
From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 13:41:32 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GJfVZB000436
for ; Wed, 16 Feb 2005 13:41:31 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GJfVnN000435
for reliable_computing-outgoing; Wed, 16 Feb 2005 13:41:31 -0600 (CST)
Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GJfNVQ000431
for ; Wed, 16 Feb 2005 13:41:28 -0600 (CST)
Received: from aragorn (aragorn [129.108.5.35])
by cs.utep.edu (8.11.7/8.11.7) with SMTP id j1GJfI723651;
Wed, 16 Feb 2005 12:41:18 -0700 (MST)
Message-Id: <200502161941.j1GJfI723651 [at] cs [dot] utep.edu>
Date: Wed, 16 Feb 2005 12:41:18 -0700 (MST)
From: Vladik Kreinovich
Reply-To: Vladik Kreinovich
Subject: NAFIPS'05 deadline extended
To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu
MIME-Version: 1.0
Content-Type: TEXT/plain; charset=us-ascii
Content-MD5: GKBaMwaxMJpt8VvMrVzQSw==
X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
Dear Friends,
I have just learned that the deadline for submitting papers to Annual
Conference of North American Information Processing Society NAFIPS'05, Ann
Arbor, Michigan, June 22-25, 2005, has been extended to February 28, 2005.
Because of the close connection between interval and fuzzy methods, this
conference is always very much interested in interval-related talks.
Just in case, the conference URL is http://www.nafips05.wayne.edu
From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 15:31:51 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GLVpFO000611
for ; Wed, 16 Feb 2005 15:31:51 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GLVp0D000610
for reliable_computing-outgoing; Wed, 16 Feb 2005 15:31:51 -0600 (CST)
Received: from poczta.polsl.pl (castor.polsl.pl [157.158.3.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GLVab0000601
for ; Wed, 16 Feb 2005 15:31:47 -0600 (CST)
Received: from pownuk ([193.25.187.101]) by poczta.polsl.pl with Microsoft SMTPSVC(6.0.3790.211);
Wed, 16 Feb 2005 22:31:33 +0100
From: "Andrzej Pownuk"
To:
Subject: RE: a book of potential interest to interval researchers
Date: Wed, 16 Feb 2005 22:31:37 +0100
Message-ID:
X-Priority: 3 (Normal)
X-MSMail-Priority: Normal
X-Mailer: Microsoft Outlook, Build 10.0.6626
In-Reply-To: <4213796C.3080008 [at] sun [dot] com>
X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180
Importance: Normal
X-OriginalArrivalTime: 16 Feb 2005 21:31:33.0961 (UTC) FILETIME=[E3230B90:01C5146E]
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
Dear interval researchers,
I have general question related to the problem,
what is interval arithmetic and what is not interval arithmetic.
As far as I know interval arithmetic
is based on the functions with interval parameters in the following form:
z=f(x) e.g. [-1, 1] = sin([-10, 10])
or
z=f(x,y)
e.g.
[2,5]=+([1,2],[1,3]) or [2,5]=[1,2]+[1,3]
[1,6]=*([1,2],[1,3]) or [1,6]=[1,2]*[1,3]
i.e. f=+,-,*,/.
However, according to my knowledge
in most of the books which are related to interval arithmetic
there are information about systems of linear interval equations.
In this case relation between input and output interval parameters is much
more complicated.
Y=hull{{x: Ax=B, A belong to [A], B belong to [B]}
We have also united solution set, tolerable solution set,
controllable solution set etc.
My question is.
****************************************************************************
Does theory of systems of linear interval equations belong
to interval arithmetic or not?
****************************************************************************
If more complicated relations on intervals
(e.g. system of linear interval equations) also belong
to interval arithmetic
then maybe all functions on intervals are some extensions
of interval arithmetic.
I suspect that the authors of the presented book
(i.e. Uncertain Input Data Problems and the Worst Scenario Method)
work on some functions with intervals or set valued parameters
(I am not sure, I do not know that book).
Then from that point of view
they are working on some extension of interval arithmetic.
Regards,
Andrzej Pownuk
---------------------------------------------
Ph.D., research associate at:
Chair of Theoretical Mechanics
Faculty of Civil Engineering
Silesian University of Technology
ul. Krzywoustego 7
44-100 Gliwice, Poland
Tel/fax: 0048 32 2371542
Mobile: 0048 606 550147
URL: http://zeus.polsl.gliwice.pl/~pownuk
E-mail: pownuk [at] zeus [dot] polsl.gliwice.pl
---------------------------------------------
I agree.
I have ordered it from Amazon. Perhaps the authors don't know
about intervals. Many people still do not.
The encouraging thing is that even point people are starting
to realize the importance of input uncertainty. This can only
be good for us. :)
Cheers,
Bill
P.S. If nothing else, this is a source of good examples for
you to use in your talk. :)
Ray Moore wrote:
> It seems odd to me that there is no mention of interval computation in
> the book.
>
> Ray Moore
>
> ----- Original Message ----- From: "Vladik Kreinovich"
> To:
> Cc:
> Sent: Wednesday, February 16, 2005 12:27 AM
> Subject: a book of potential interest to interval researchers
>
>
>> Forwarding, from NA Digest
>> ******************************************
>> From: Jan Chleboun
>> Date: Wed, 9 Feb 2005 12:09:50 +0100 (CET)
>> Subject: New Book on Uncertain Input Data
>>
>> Uncertain Input Data Problems and the Worst Scenario Method
>> by Ivan Hlavacek, Jan Chleboun, and Ivo Babuska;
>> North-Holland Series in Applied Mathematics and Mechanics, Volume 46,
>> Elsevier, Amsterdam, December 2004.
>> Hardback, xxvi+458 pages, ISBN: 0-444-51435-X
>>
>> This book deals with the impact of uncertainty in input data on the
>> outputs of mathematical models. Uncertain inputs as scalars, tensors,
>> functions, or domain boundaries are considered. In practical terms,
>> material parameters or constitutive laws, for instance, are uncertain,
>> and
>> quantities as local temperature, local mechanical stress, or local
>> displacement are monitored. The goal of the worst scenario method is to
>> extremize the quantity over the set of uncertain input data.
>>
>> A general mathematical scheme of the worst scenario method, including
>> approximation by finite element methods, is presented, and then
>> applied to
>> various state problems modeled by differential equations or variational
>> inequalities: nonlinear heat flow, Timoshenko beam vibration and
>> buckling,
>> plate buckling, contact problems in elasticity and thermoelasticity with
>> and without friction, and various models of plastic deformation, to list
>> some of the topics. Dozens of examples, figures, and tables are included.
>>
>> More details can be found at
>> http://books.elsevier.com/elsevier/?isbn=044451435X
>>
>> Jan Chleboun
>> Mathematical Institute
>> Academy of Sciences
>> Zitna 25 ( TeX: \v{Z}itn\'a )
>> 115 67 Prague 1
>> Czech Republic
>> e-mail: chleb [at] math [dot] cas.cz
>>
>>
>
From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 15:50:08 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GLo7hc000804
for ; Wed, 16 Feb 2005 15:50:07 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GLo7Zo000803
for reliable_computing-outgoing; Wed, 16 Feb 2005 15:50:07 -0600 (CST)
Received: from lakermmtao10.cox.net (lakermmtao10.cox.net [68.230.240.29])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GLnvlC000799
for ; Wed, 16 Feb 2005 15:50:03 -0600 (CST)
Received: from Inspiron-8200 ([68.226.133.93]) by lakermmtao10.cox.net
(InterMail vM.6.01.04.00 201-2131-117-20041022) with SMTP
id <20050216214950.YRVI17761.lakermmtao10.cox.net@Inspiron-8200>;
Wed, 16 Feb 2005 16:49:50 -0500
Message-Id: <2.2.32.20050216214944.0093e554 [at] pop [dot] louisiana.edu>
X-Sender: rbk5287 [at] pop [dot] louisiana.edu
X-Mailer: Windows Eudora Pro Version 2.2 (32)
Mime-Version: 1.0
Content-Type: text/plain; charset="iso-8859-1"
Date: Wed, 16 Feb 2005 15:49:44 -0600
To: "Andrzej Pownuk" ,
From: "R. Baker Kearfott"
Subject: RE: a book of potential interest to interval researchers
Content-Transfer-Encoding: 8bit
X-MIME-Autoconverted: from quoted-printable to 8bit by interval.louisiana.edu id j1GLo4lC000800
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
All,
If the criterion to "belonging" to interval arithmetic is whether
or not interval researchers work on it, then the result is a
resounding "yes." Ask Jiri Rohn, G{\"o}tz Alefeld, or Sergey Shary,
(among others) for example.
I view "interval arithmetic" as striving to compute sharp bounds
on ranges, in a way that takes account of machine arithmetic. This
may, at times, go beyond use of the pre-programmed four basic
"arithmetic" operations; I think the goal should take us wherever
is appropriate, and we should not get too stuck on what the subject
is called, except, of course, if it would otherwise lead
to technical confusion, or for promotional purposes :-)
Best regards,
Baker
At 10:31 PM 2/16/2005 +0100, Andrzej Pownuk wrote:
>Dear interval researchers,
>
>I have general question related to the problem,
>what is interval arithmetic and what is not interval arithmetic.
>
>As far as I know interval arithmetic
>is based on the functions with interval parameters in the following form:
>
>z=f(x) e.g. [-1, 1] = sin([-10, 10])
>
>or
>
>z=f(x,y)
>e.g.
>[2,5]=+([1,2],[1,3]) or [2,5]=[1,2]+[1,3]
>
>[1,6]=*([1,2],[1,3]) or [1,6]=[1,2]*[1,3]
>
>i.e. f=+,-,*,/.
>
>However, according to my knowledge
>in most of the books which are related to interval arithmetic
>there are information about systems of linear interval equations.
>In this case relation between input and output interval parameters is much
>more complicated.
>
>Y=hull{{x: Ax=B, A belong to [A], B belong to [B]}
>
>We have also united solution set, tolerable solution set,
>controllable solution set etc.
>
>My question is.
>
>****************************************************************************
>Does theory of systems of linear interval equations belong
>to interval arithmetic or not?
>****************************************************************************
>
>If more complicated relations on intervals
>(e.g. system of linear interval equations) also belong
>to interval arithmetic
>then maybe all functions on intervals are some extensions
>of interval arithmetic.
>
>I suspect that the authors of the presented book
>(i.e. Uncertain Input Data Problems and the Worst Scenario Method)
>work on some functions with intervals or set valued parameters
>(I am not sure, I do not know that book).
>Then from that point of view
>they are working on some extension of interval arithmetic.
>
>Regards,
>
>Andrzej Pownuk
>
>---------------------------------------------
>Ph.D., research associate at:
>Chair of Theoretical Mechanics
>Faculty of Civil Engineering
>Silesian University of Technology
>ul. Krzywoustego 7
>44-100 Gliwice, Poland
>
>Tel/fax: 0048 32 2371542
>Mobile: 0048 606 550147
>
>URL: http://zeus.polsl.gliwice.pl/~pownuk
>E-mail: pownuk [at] zeus [dot] polsl.gliwice.pl
>---------------------------------------------
>
>I agree.
>
>I have ordered it from Amazon. Perhaps the authors don't know
>about intervals. Many people still do not.
>
>The encouraging thing is that even point people are starting
>to realize the importance of input uncertainty. This can only
>be good for us. :)
>
>Cheers,
>
>Bill
>
>P.S. If nothing else, this is a source of good examples for
>you to use in your talk. :)
>
>
>Ray Moore wrote:
>
>> It seems odd to me that there is no mention of interval computation in
>> the book.
>>
>> Ray Moore
>>
>> ----- Original Message ----- From: "Vladik Kreinovich"
>
>> To:
>> Cc:
>> Sent: Wednesday, February 16, 2005 12:27 AM
>> Subject: a book of potential interest to interval researchers
>>
>>
>>> Forwarding, from NA Digest
>>> ******************************************
>>> From: Jan Chleboun
>>> Date: Wed, 9 Feb 2005 12:09:50 +0100 (CET)
>>> Subject: New Book on Uncertain Input Data
>>>
>>> Uncertain Input Data Problems and the Worst Scenario Method
>>> by Ivan Hlavacek, Jan Chleboun, and Ivo Babuska;
>>> North-Holland Series in Applied Mathematics and Mechanics, Volume 46,
>>> Elsevier, Amsterdam, December 2004.
>>> Hardback, xxvi+458 pages, ISBN: 0-444-51435-X
>>>
>>> This book deals with the impact of uncertainty in input data on the
>>> outputs of mathematical models. Uncertain inputs as scalars, tensors,
>>> functions, or domain boundaries are considered. In practical terms,
>>> material parameters or constitutive laws, for instance, are uncertain,
>>> and
>>> quantities as local temperature, local mechanical stress, or local
>>> displacement are monitored. The goal of the worst scenario method is to
>>> extremize the quantity over the set of uncertain input data.
>>>
>>> A general mathematical scheme of the worst scenario method, including
>>> approximation by finite element methods, is presented, and then
>>> applied to
>>> various state problems modeled by differential equations or variational
>>> inequalities: nonlinear heat flow, Timoshenko beam vibration and
>>> buckling,
>>> plate buckling, contact problems in elasticity and thermoelasticity with
>>> and without friction, and various models of plastic deformation, to list
>>> some of the topics. Dozens of examples, figures, and tables are included.
>>>
>>> More details can be found at
>>> http://books.elsevier.com/elsevier/?isbn=044451435X
>>>
>>> Jan Chleboun
>>> Mathematical Institute
>>> Academy of Sciences
>>> Zitna 25 ( TeX: \v{Z}itn\'a )
>>> 115 67 Prague 1
>>> Czech Republic
>>> e-mail: chleb [at] math [dot] cas.cz
>>>
>>>
>>
>
>
>
>
---------------------------------------------------------------
R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax)
(337) 482-5270 (work) (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------
From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 17:03:08 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GN38OY001064
for ; Wed, 16 Feb 2005 17:03:08 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GN38AH001063
for reliable_computing-outgoing; Wed, 16 Feb 2005 17:03:08 -0600 (CST)
Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GN2xHA001059
for ; Wed, 16 Feb 2005 17:03:05 -0600 (CST)
Received: from aragorn (aragorn [129.108.5.35])
by cs.utep.edu (8.11.7/8.11.7) with SMTP id j1GN2oN25309;
Wed, 16 Feb 2005 16:02:50 -0700 (MST)
Message-Id: <200502162302.j1GN2oN25309 [at] cs [dot] utep.edu>
Date: Wed, 16 Feb 2005 16:02:50 -0700 (MST)
From: Vladik Kreinovich
Reply-To: Vladik Kreinovich
Subject: RE: a book of potential interest to interval researchers
To: reliable_computing [at] interval [dot] louisiana.edu, andrzej.pownuk [at] polsl [dot] pl
MIME-Version: 1.0
Content-Type: TEXT/plain; charset=us-ascii
Content-MD5: 29vrR+ZyduZ8XBYIVP/GBw==
X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
Dear Andrzej,
Just one comment to what Baker said: united solution set is EXACTLY what
interval computations is about.
In general, one of the main problems of interval computation is, given a
function f(x1,...,xn) and intervals [x1],...,[xn], find teh range of f on these
intervals.
For linear equations, the inputs are coefficients of the matrix A and of the
right-hand side b, and i-th function is a function that, given A and b, returns
i-th component of the solution. Then the range of this function is exactly i-th
component of the united solution set.
This is, by the way, how we introduce linear systems in our complexity of
interval computations book (written with Jiri Rohn).
Vladik
> From: "Andrzej Pownuk"
> To:
> Subject: RE: a book of potential interest to interval researchers
> Date: Wed, 16 Feb 2005 22:31:37 +0100
> X-Priority: 3 (Normal)
> X-MSMail-Priority: Normal
> X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180
> Importance: Normal
> X-OriginalArrivalTime: 16 Feb 2005 21:31:33.0961 (UTC)
FILETIME=[E3230B90:01C5146E]
>
> Dear interval researchers,
>
> I have general question related to the problem,
> what is interval arithmetic and what is not interval arithmetic.
>
> As far as I know interval arithmetic
> is based on the functions with interval parameters in the following form:
>
> z=f(x) e.g. [-1, 1] = sin([-10, 10])
>
> or
>
> z=f(x,y)
> e.g.
> [2,5]=+([1,2],[1,3]) or [2,5]=[1,2]+[1,3]
>
> [1,6]=*([1,2],[1,3]) or [1,6]=[1,2]*[1,3]
>
> i.e. f=+,-,*,/.
>
> However, according to my knowledge
> in most of the books which are related to interval arithmetic
> there are information about systems of linear interval equations.
> In this case relation between input and output interval parameters is much
> more complicated.
>
> Y=hull{{x: Ax=B, A belong to [A], B belong to [B]}
>
> We have also united solution set, tolerable solution set,
> controllable solution set etc.
>
> My question is.
>
> ****************************************************************************
> Does theory of systems of linear interval equations belong
> to interval arithmetic or not?
> ****************************************************************************
>
> If more complicated relations on intervals
> (e.g. system of linear interval equations) also belong
> to interval arithmetic
> then maybe all functions on intervals are some extensions
> of interval arithmetic.
>
> I suspect that the authors of the presented book
> (i.e. Uncertain Input Data Problems and the Worst Scenario Method)
> work on some functions with intervals or set valued parameters
> (I am not sure, I do not know that book).
> Then from that point of view
> they are working on some extension of interval arithmetic.
>
> Regards,
>
> Andrzej Pownuk
From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Feb 17 06:44:23 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1HCiNNi002568
for ; Thu, 17 Feb 2005 06:44:23 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1HCiNR1002567
for reliable_computing-outgoing; Thu, 17 Feb 2005 06:44:23 -0600 (CST)
Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1HCiKE0002563
for ; Thu, 17 Feb 2005 06:44:20 -0600 (CST)
Received: (from rbk5287@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1HCiKDE002562
for reliable_computing [at] interval [dot] louisiana.edu; Thu, 17 Feb 2005 06:44:20 -0600 (CST)
Received: from scanner2.ics.uci.edu (scanner2.ics.uci.edu [128.195.1.36])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1H5F1B2001568
for ; Wed, 16 Feb 2005 23:15:10 -0600 (CST)
Received: from igor.ics.uci.edu (wayne [at] igor [dot] ics.uci.edu [128.195.4.119])
by scanner2.ics.uci.edu (8.12.10/8.12.10) with ESMTP id j1H5DaAH016489
for ; Wed, 16 Feb 2005 21:13:37 -0800 (PST)
Date: Wed, 16 Feb 2005 21:13:36 -0800
From: Wayne Hayes
To: reliable_computing [at] interval [dot] louisiana.edu
Subject: Does a more recent version of "UniCalc" exist?
Message-ID: <20050217051336.GA28708 [at] igor [dot] ics.uci.edu>
References: <2.2.32.20041102155117.00a19374 [at] pop [dot] louisiana.edu>
Mime-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Disposition: inline
In-Reply-To: <2.2.32.20041102155117.00a19374 [at] pop [dot] louisiana.edu>
User-Agent: Mutt/1.4i
X-ICS-MailScanner: Found to be clean
X-ICS-MailScanner-SpamCheck: not spam (whitelisted),
SpamAssassin (score=-96.69, required 5, MSGID_FROM_MTA_SHORT,
USER_IN_WHITELIST)
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
Hello. I've been playing with Jeff Tupper's wonderful GrafEq program
(http://www.peda.com/grafeq), but I would like to be able to solve
problems in more than two variables. Some searching around finds
a program called UniCalc,
http://archives.math.utk.edu/software/msdos/miscellaneous/unicalc/.html
although it's a little archaic (from about 1995, only working under
MS-DOS). Is there anything a bit more modern that combines the
versatility of UniCalc with a more modern interface, and presumably
updated algorithms, such as those found in GrafEq?
- Wayne Hayes
From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Feb 17 06:45:37 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1HCjaVI002605
for ; Thu, 17 Feb 2005 06:45:36 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1HCja6h002604
for reliable_computing-outgoing; Thu, 17 Feb 2005 06:45:36 -0600 (CST)
Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1HCjXv2002600
for ; Thu, 17 Feb 2005 06:45:33 -0600 (CST)
Received: (from rbk5287@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1HCjXEb002599
for reliable_computing [at] interval [dot] louisiana.edu; Thu, 17 Feb 2005 06:45:33 -0600 (CST)
Received: from matsrv.math.cas.cz (matsrv.math.cas.cz [147.231.88.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1H8ZG5g001847
for ; Thu, 17 Feb 2005 02:35:22 -0600 (CST)
Received: from matsrv.math.cas.cz (matsrv.math.cas.cz [127.0.0.1])
by matsrv.math.cas.cz (8.12.11/8.12.11) with ESMTP id j1H8Z4pa018955;
Thu, 17 Feb 2005 09:35:04 +0100
Received: from localhost (chleb@localhost)
by matsrv.math.cas.cz (8.12.11/8.12.11/Submit) with ESMTP id j1H8Z019018913;
Thu, 17 Feb 2005 09:35:00 +0100
Date: Thu, 17 Feb 2005 09:35:00 +0100 (CET)
From: Jan Chleboun
To: Vladik Kreinovich
cc: Ray Moore ,
"G. William Walster" ,
reliable_computing [at] interval [dot] louisiana.edu, pardalos [at] cao [dot] ise.ufl.edu
Subject: Re: a book of potential interest to interval researchers
In-Reply-To: <4213796C.3080008 [at] sun [dot] com>
Message-ID:
References: <200502160527.j1G5RBt19348 [at] cs [dot] utep.edu> <000701c5141f$364f8550$1702a8c0@Moore>
<4213796C.3080008 [at] sun [dot] com>
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed
X-Virus-Scanned: ClamAV 0.82/707/Wed Feb 16 23:00:07 2005 on matsrv.math.cas.cz
X-Virus-Status: Clean
X-Spam-Status: No, hits=-4.9 required=5.0 tests=BAYES_00 autolearn=no
version=2.64
X-Spam-Checker-Version: SpamAssassin 2.64 (2004-01-11) on matsrv.math.cas.cz
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
Dear Professors Kreinovich, Moore, Pardalos, and Walster,
> It seems odd to me that there is no mention of interval computation in
> the book.
>
You are right, interval arithmetic is only briefly mentioned
at page xx and page 9 of the book.
However, intervals instead of crisp values appear in Timoshenko beam
problems or a plasticity model, for instance. The related mathematical
problems are solved analytically or numerically using standard computer
arithmetic.
With best regards,
Jan Chleboun
******************************
Jan Chleboun
Mathematical Institute
Academy of Sciences
Zitna 25 ( TeX: \v{Z}itn\'a )
115 67 Prague 1
Czech Republic
e-mail: chleb [at] math [dot] cas.cz
******************************
From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Feb 17 08:30:13 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1HEUDeE002947
for ; Thu, 17 Feb 2005 08:30:13 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1HEUDgp002946
for reliable_computing-outgoing; Thu, 17 Feb 2005 08:30:13 -0600 (CST)
Received: from zmit1.ippt.gov.pl (zmit1.ippt.gov.pl [148.81.53.8])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1HEU3A9002942
for ; Thu, 17 Feb 2005 08:30:09 -0600 (CST)
Received: (from zkulpa@localhost) by zmit1.ippt.gov.pl (8.8.5/8.7.3-zmit) id PAA23799 for reliable_computing [at] interval [dot] louisiana.edu; Thu, 17 Feb 2005 15:24:39 +0100 (MET)
Date: Thu, 17 Feb 2005 15:24:39 +0100 (MET)
From: Zenon Kulpa
Message-Id: <200502171424.PAA23799 [at] zmit1 [dot] ippt.gov.pl>
To: reliable_computing [at] interval [dot] louisiana.edu
Subject: RE: a book of potential interest to interval researchers
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
> From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 22:27:57 2005
> From: "Andrzej Pownuk"
>
[...]>
> My question is.
>
> ******************************************************************
> Does theory of systems of linear interval equations belong
> to interval arithmetic or not?
> ******************************************************************
>
Positively yes, I presume...
[...]
> I suspect that the authors of the presented book
> (i.e. Uncertain Input Data Problems and the Worst Scenario Method)
> work on some functions with intervals or set valued parameters
> (I am not sure, I do not know that book).
> Then from that point of view
> they are working on some extension of interval arithmetic.
>
Certainly, as far as I can judge from the information posted
to the list, they are certainly working on interval arithmetic.
That is not the problem - the problem is, as I understand
the post of prof. Moore, that they do not mention/advertise
that fact (or only very accidentally, as a recent post
by Jan Chleboun clarifies).
-- Zenon Kulpa
From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Feb 17 08:38:24 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1HEcOrT003066
for ; Thu, 17 Feb 2005 08:38:24 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1HEcNjN003065
for reliable_computing-outgoing; Thu, 17 Feb 2005 08:38:23 -0600 (CST)
Received: from ms-smtp-03-eri0.ohiordc.rr.com (ms-smtp-03-smtplb.ohiordc.rr.com [65.24.5.137])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1HEc9hR003061
for ; Thu, 17 Feb 2005 08:38:20 -0600 (CST)
Received: from Moore (wor226111.columbus.rr.com [204.210.226.111])
by ms-smtp-03-eri0.ohiordc.rr.com (8.12.10/8.12.7) with SMTP id j1HEc2wZ009149;
Thu, 17 Feb 2005 09:38:03 -0500 (EST)
Message-ID: <000901c514fe$4f3fb0f0$1702a8c0@Moore>
From: "Ray Moore"
To: "Zenon Kulpa" ,
References: <200502171424.PAA23799 [at] zmit1 [dot] ippt.gov.pl>
Subject: Re: a book of potential interest to interval researchers
Date: Thu, 17 Feb 2005 09:38:12 -0500
MIME-Version: 1.0
Content-Type: text/plain;
format=flowed;
charset="iso-8859-1";
reply-type=original
Content-Transfer-Encoding: 7bit
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
Perhaps we should all read the book before we get too involved in discussion
of it. We are told that we should not judge a book by its cover.
Ray Moore
----- Original Message -----
From: "Zenon Kulpa"
To:
Sent: Thursday, February 17, 2005 9:24 AM
Subject: RE: a book of potential interest to interval researchers
>> From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 22:27:57
>> 2005
>> From: "Andrzej Pownuk"
>>
> [...]>
>> My question is.
>>
>> ******************************************************************
>> Does theory of systems of linear interval equations belong
>> to interval arithmetic or not?
>> ******************************************************************
>>
> Positively yes, I presume...
>
> [...]
>> I suspect that the authors of the presented book
>> (i.e. Uncertain Input Data Problems and the Worst Scenario Method)
>> work on some functions with intervals or set valued parameters
>> (I am not sure, I do not know that book).
>> Then from that point of view
>> they are working on some extension of interval arithmetic.
>>
> Certainly, as far as I can judge from the information posted
> to the list, they are certainly working on interval arithmetic.
> That is not the problem - the problem is, as I understand
> the post of prof. Moore, that they do not mention/advertise
> that fact (or only very accidentally, as a recent post
> by Jan Chleboun clarifies).
>
> -- Zenon Kulpa
>
From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Feb 17 10:15:40 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1HGFe9S003276
for ; Thu, 17 Feb 2005 10:15:40 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1HGFeAt003275
for reliable_computing-outgoing; Thu, 17 Feb 2005 10:15:40 -0600 (CST)
Received: from mail-mta.sunlabs.com (dyn50.sunlabs.com [204.153.12.50])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1HGFU0u003271
for ; Thu, 17 Feb 2005 10:15:36 -0600 (CST)
Received: from mail.sunlabs.com ([152.70.2.186]) by mail-mta.sfvic.sunlabs.com
(Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004))
with ESMTP id <0IC200734D5E9C00@mail-mta.sfvic.sunlabs.com> for
reliable_computing [at] interval [dot] louisiana.edu; Thu,
17 Feb 2005 08:15:14 -0800 (PST)
Received: from [129.146.72.246] by mail.sunlabs.com
(Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004))
with ESMTPSA id <0IC200CE2D5B8A10 [at] mail [dot] sunlabs.com> for
reliable_computing [at] interval [dot] louisiana.edu; Thu,
17 Feb 2005 08:15:11 -0800 (PST)
Date: Thu, 17 Feb 2005 08:15:14 -0800
From: "G. William Walster"
Subject: Re: Does a more recent version of "UniCalc" exist?
In-reply-to: <20050217051336.GA28708 [at] igor [dot] ics.uci.edu>
To: Wayne Hayes
Cc: reliable_computing [at] interval [dot] louisiana.edu
Reply-to: Bill.Walster [at] sun [dot] com
Message-id: <4214C312.6070304 [at] sun [dot] com>
Organization: Sun Microsystems Laboratories
MIME-version: 1.0
Content-type: text/plain; charset=us-ascii; format=flowed
Content-transfer-encoding: 7BIT
X-Accept-Language: en-us, en
References: <2.2.32.20041102155117.00a19374 [at] pop [dot] louisiana.edu>
<20050217051336.GA28708 [at] igor [dot] ics.uci.edu>
User-Agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X Mach-O; en-US; rv:1.7)
Gecko/20040616
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
Wayne,
Check out Graphing Calculator at
The good news is that it has a much richer
interface and the algorithms use intervals.
The bad news is that the algorithms are *not*
rigorous. What would be cool is to have the
interface and versitility of Graphing Calculator
with the rigor of GrafEq.
Perhaps the community could begin to lobby for
such a development.
Cheers,
Bill
Wayne Hayes wrote:
> Hello. I've been playing with Jeff Tupper's wonderful GrafEq program
> (http://www.peda.com/grafeq), but I would like to be able to solve
> problems in more than two variables. Some searching around finds
> a program called UniCalc,
>
> http://archives.math.utk.edu/software/msdos/miscellaneous/unicalc/.html
>
> although it's a little archaic (from about 1995, only working under
> MS-DOS). Is there anything a bit more modern that combines the
> versatility of UniCalc with a more modern interface, and presumably
> updated algorithms, such as those found in GrafEq?
>
> - Wayne Hayes
>
From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Feb 18 03:44:49 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1I9imfb004844
for ; Fri, 18 Feb 2005 03:44:48 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1I9imWU004843
for reliable_computing-outgoing; Fri, 18 Feb 2005 03:44:48 -0600 (CST)
Received: from mx.iis.nsk.su (mxalt.iis.nsk.su [194.226.177.83])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1I9iZ5O004838
for ; Fri, 18 Feb 2005 03:44:43 -0600 (CST)
Received: from [192.168.1.135] (bream.rriai.org.ru [194.226.177.135])
(authenticated bits=0)
by mx.iis.nsk.su (8.12.9/8.12.9) with ESMTP id j1I9i0E8016617;
Fri, 18 Feb 2005 15:44:07 +0600 (NOVT)
(envelope-from pes [at] iis [dot] nsk.su)
Message-ID: <4215B8E5.8090207 [at] iis [dot] nsk.su>
Date: Fri, 18 Feb 2005 15:44:05 +0600
From: Evgueni Petrov
User-Agent: Mozilla Thunderbird 1.0 (Windows/20041206)
X-Accept-Language: en-us, en
MIME-Version: 1.0
To: Wayne Hayes
CC: reliable_computing [at] interval [dot] louisiana.edu
Subject: Re: Does a more recent version of "UniCalc" exist?
References: <2.2.32.20041102155117.00a19374 [at] pop [dot] louisiana.edu> <20050217051336.GA28708 [at] igor [dot] ics.uci.edu>
In-Reply-To: <20050217051336.GA28708 [at] igor [dot] ics.uci.edu>
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
Hello Wayne,
Here are the facts concerning Unicalc that i am aware of.
Yes, Unicalc is accessible through web-interface at
http://speedy.iis.nsk.su.
Please keep in mind that this site is not maintained regularly.
You will find two solvers there: Unicalc3 (the one you mention) and a
beta version of Unicalc5.
Please see Introduction for general instructions on usage.
All your runs of Unicalc will be limited to 15 variables and 5 seconds
of CPU time.
Hopefully, Unicalc5 will be released April-May 2005.
Best regards,
Evgueni Petrov.
Wayne Hayes wrote:
>Hello. I've been playing with Jeff Tupper's wonderful GrafEq program
>(http://www.peda.com/grafeq), but I would like to be able to solve
>problems in more than two variables. Some searching around finds
>a program called UniCalc,
>
> http://archives.math.utk.edu/software/msdos/miscellaneous/unicalc/.html
>
>although it's a little archaic (from about 1995, only working under
>MS-DOS). Is there anything a bit more modern that combines the
>versatility of UniCalc with a more modern interface, and presumably
>updated algorithms, such as those found in GrafEq?
>
> - Wayne Hayes
>
From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Feb 18 04:40:37 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1IAean8005347
for ; Fri, 18 Feb 2005 04:40:36 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1IAeauY005346
for reliable_computing-outgoing; Fri, 18 Feb 2005 04:40:36 -0600 (CST)
Received: from interferon.mpi-sb.mpg.de (mail.mpi-sb.mpg.de [139.19.1.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1IAeRZE005342
for ; Fri, 18 Feb 2005 04:40:33 -0600 (CST)
Received: from amavis by interferon.mpi-sb.mpg.de with scanned-ok (Exim 3.36 #1 (Debian))
id 1D25Yb-0002tW-00
for ; Fri, 18 Feb 2005 11:40:21 +0100
Received: from mpino2303.ag2.mpi-sb.mpg.de ([139.19.24.75])
by interferon.mpi-sb.mpg.de with esmtp (Exim 3.36 #1 (Debian))
id 1D25YX-0002sW-00; Fri, 18 Feb 2005 11:40:17 +0100
Subject: Re: Does a more recent version of "UniCalc" exist?
From: Stefan Ratschan
To: Wayne Hayes
Cc: reliable_computing [at] interval [dot] louisiana.edu
In-Reply-To: <20050217051336.GA28708 [at] igor [dot] ics.uci.edu>
References: <2.2.32.20041102155117.00a19374 [at] pop [dot] louisiana.edu>
<20050217051336.GA28708 [at] igor [dot] ics.uci.edu>
Content-Type: text/plain
Date: Fri, 18 Feb 2005 11:39:46 +0100
Message-Id: <1108723187.3498.18.camel@localhost>
Mime-Version: 1.0
X-Mailer: Evolution 2.0.3
Content-Transfer-Encoding: 7bit
X-Virus-Scanned: by AMaViS perl-11
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
On Mit, 2005-02-16 at 21:13 -0800, Wayne Hayes wrote:
> Hello. I've been playing with Jeff Tupper's wonderful GrafEq program
> (http://www.peda.com/grafeq), but I would like to be able to solve
> problems in more than two variables.
Our solver can compute validated over- and underapproximations of the
projection to 2-dimensional space of higher-dimensional solution sets of
systems of inequalities: http://www.mpi-sb.mpg.de/~ratschan/rsolver/
Try to enter things like
EXISTS [z] [[-2,2]] [ x^2+y^2+z^2<=1 /\ z>y ];
in the provided web interface.
However, please be aware that all of this is still a research prototype.
Stefan Ratschan
From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Feb 19 06:16:58 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1JCGvjw007465
for ; Sat, 19 Feb 2005 06:16:58 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1JCGvM5007464
for reliable_computing-outgoing; Sat, 19 Feb 2005 06:16:57 -0600 (CST)
Received: from relay.pair.com (relay00.pair.com [209.68.1.20])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with SMTP id j1JCGmA2007460
for ; Sat, 19 Feb 2005 06:16:54 -0600 (CST)
Date: Sat, 19 Feb 2005 06:16:49 -0600 (CST)
Message-Id: <200502191216.j1JCGmA2007460 [at] interval [dot] louisiana.edu>
Received: (qmail 7464 invoked from network); 19 Feb 2005 12:15:37 -0000
Received: from unknown (HELO peda.com) (unknown)
by unknown with SMTP; 19 Feb 2005 12:15:37 -0000
X-pair-Authenticated: 209.68.1.35
From: Jeff Tupper
To:
Subject: Re: Does a more recent version of "UniCalc" exist?
Sender: owner-reliable_computing [at] interval [dot] louisiana.edu
Precedence: bulk
At 9:13 PM -0800 2/16/05, Wayne Hayes wrote:
>I've been playing with Jeff Tupper's wonderful GrafEq program
>(http://www.peda.com/grafeq), but I would like to be able to solve
>problems in more than two variables.
I'm trying to write up papers on some of the graphing programs I've
been working on. I've made good progress towards that end with clg
(in that I've submitted a first paper on it to a conference in the U.S.),
which is another two-dimensional program (which was used to produce
some of the illustrations in Hansen and Walster's "Global
Optimization Using Interval Analysis"; I'm giving an introductory
talk that discusses some aspects of clg here in Antwerp next week
[Annie Cuyt has kindly brought me over here for a few weeks] and back
at Toronto in a few weeks). After I've done a bit more writing on
clg, I'm hoping to bring one of my older programs that displays
three-dimensional views out of hibernation.
Jeff
From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Feb 21 08:52:42 2005
Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1LEqgq0012155
for ; Mon, 21 Feb 2005 08:52:42 -0600 (CST)
Received: (from daemon@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1LEqfLX012154
for reliable_computing-outgoing; Mon, 21 Feb 2005 08:52:41 -0600 (CST)
Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1LEqcha012146
for ; Mon, 21 Feb 2005 08:52:38 -0600 (CST)
Received: (from rbk5287@localhost)
by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1LEqcRL012145
for reliable_computing [at] interval [dot] louisiana.edu; Mon, 21 Feb 2005 08:52:38 -0600 (CST)
Received: from scanner2.ics.uci.edu (scanner2.ics.uci.edu [128.195.1.36])
by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1I30hxO004301
for ; Thu, 17 Feb 2005 21:00:49 -0600 (CST)
Received: from igor.ics.uci.edu (wayne [at] igor [dot] ics.uci.edu [128.195.4.119])
by scanner2.ics.uci.edu (8.12.10/8.12.10) with ESMTP id j1I2x3AH000182
for ; Thu, 17 Feb 2005 18:59:03 -0800 (PST)
Date: Thu, 17 Feb 2005 18:59:03 -0800
From: Wayne Hayes