Subject: Reliable Computing, vol. 9, issue 1, 2003
Date: Sat, 23 Nov 2002 10:19:57 +0300
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Reliable Computing=20
Volume 9, issue 1, 2003
Mathematical Research
Diagrammatic Analysis of Interval Linear Equations: =20
Part I: Basic Notions and the One-Dimensional Case
Zenon Kulpa=20
1-20
Controlling the Wrapping Effect in the Solution=20
of ODEs for Asteroids
Jens Hoefkens, Martin Berz, Kyoko Makino
21-41
=20
Review
Taylor Forms - Use and Limits
Arnold Neumaier
43-79
=20
Information
COCOS'02: A Workshop on Global Constrained Optimization and Constraint
Satisfaction
R. Baker Kearfott
81-87
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charset="koi8-r"
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=
Reliable=20
Computing

Volume 9, =
issue=20
1, 2003

=
Mathematical=20
Research

Diagrammatic Analysis of Interval =
Linear=20
Equations: &nb=
sp;=20

Part I: Basic Notions and the One-Dimensional Case

Zenon Kulpa=20

1-20

Controlling the Wrapping Effect =
in the=20
Solution

of ODEs for Asteroids

Jens Hoefkens, Martin Berz, Kyoko=20
Makino

21-41

=
=20

&nb=
sp; =20
Review

Taylor Forms - Use and =
Limits

Arnold=20
Neumaier

43-79

=20

&nb=
sp; =20
Information

COCOS'02: A Workshop on Global =
Constrained=20
Optimization and Constraint

Satisfaction

R. Baker=20
Kearfott

81-87

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From: Vladik Kreinovich
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Subject: from NA Digest: interval computations mentioned
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From: Theodore Simos
Date: Mon, 18 Nov 2002 03:00:47 +0200
Subject: Conference in Cambridge on Numerical Analysis & Computational Math
FIRST ANNOUNCEMENT AND CALL FOR PAPERS
International Conference on NUMERICAL ANALYSIS & COMPUTATIONAL
MATHEMATICS (NACoM-2003)
May 23-24-25-26, 2003
Anglia Polytechnic University (APU), Cambridge, UK
http://www.apu.ac.uk/appsci/maths/NACoM-2003/
The multidisciplinary field of Numerical Analysis and Computational
Mathematics is long suffering from major delays in the publication of
original papers. In most cases it takes at least 2 to 3 years for a
paper to be accepted and the situation seems to get worse by the year.
The NACoM-2003 will address this problem, as follows:
1) This first time the NACoM Conference will serve as the medium for the
official LAUNCH of a new WILEY JOURNAL on "APPLIED NUMERICAL ANALYSIS
AND COMPUTATIONAL MATHEMATICS (ANACM)" (Editor-in-Chief T.E. SIMOS).
Generally, in ANACM it is expected that the time between a paper
submission and its acceptance for publication to be around 6 months.
ANACM will be registered with the ISI CITATION INDEX without delay.
2) The NACoM-2003 Conference is expected to attract very high quality
papers and a refereed selection of them will be published in the two
special issues of the new journal.
3) This will be an excellent opportunity to MEET IN PERSON members of
the ANACM EDITORIAL BOARD. Furthermore, high-ranking representatives
from Wiley-Europe will be present and will address the participants.
MAIN TOPICS
Numerical ODEs, Numerical PDEs (inc. BVPs), Differential Algebraic
Equations, Numerical Stochastic Differential Equations, Approximation,
Numerical Linear Algebra, Numerical Integral Equations, Error Analysis
and Interval Analysis, Difference
Equations and Recurrence Relations, Numerical problems in Dynamical
Systems, Applications to the Sciences (Computational
Physics-Chemistry-Engineering etc.), Scientific Computing and
Algorithms, Numerical methods in Fourier analysis.
GENERAL CHAIR & ORGANISER
Dr Georgios Psihoyios, Anglia Pol. University, Cambridge, UK
VICE-CHAIRS
Prof. Theodore E. Simos, University of Peloponnisos, Greece
Boz Kempski, Anglia Pol. University, Cambridge, UK
PLENARY SPEAKERS (to be finalised)
Prof. J.R. Cash, Imperial College, London, UK.
Prof. A. Cuyt, University of Antwerp, Belgium.
Prof. B. Fischer, Medical University of Luebeck, Germany.
Prof. M. Hochbruck, University of Duesseldorf, Germany.
Prof. W.F. Mitchell, National Institute of Standards & Technology, USA.
Prof. G. Vanden Berghe, University of Gent, Belgium.
Prof. G.A. Watson, University of Dundee, UK
CALL FOR PAPERS & EXPRESSION OF INTEREST
Submission of original papers is invited for the NACoM-2003 Conference.
Please initially submit an ABSTRACT OF UP TO FOUR A4 PAGES directly to
the General Chair (g.y.psihoyios [at] apu [dot] ac.uk) by February 28, 2003. Please
send a standard Latex article style abstract without page numbers. For
further instructions please refer to the WEBSITE. Only electronic
submission of abstracts will be accepted.
DEADLINES
Submission of Abstract (on or before): February 28, 2003
Submission of Mini-symposia proposals: February 28, 2003
Abstracts refereed selection by: March 20, 2003
Submission of full-length Papers: To be announced
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Dear Friends, This is the 2003 conference about which I mentioned that the 2004
oen can be back-toback with Denmark meeting.
Vladik
***********************************************************************
XXXI Summer School "Advanced Problems in Mechanics"
June 23-July 2, 2003, St. Petersburg, Russia
First Announcement
A P M 2 0 0 3
http://www.eng.abdn.ac.uk/~apm/2003
To receive our announcements, please send a void e-mail with the subject
"subscribe" to
apm [at] eng [dot] abdn.ac.uk
We will be grateful if you spread this announcement among your colleagues
GENERAL INFORMATION
The Summer school Advanced Problems in Mechanics 2003 is organized by the
Institute for Problems in Mechanical Engineering of the Russian Academy of
Sciences (IPME RAS) under the patronage of the Russian Academy of Sciences and
with information support of Gesellschaft fuer Angewandte Mathematik und
Mechanik (GAMM). The main purpose of the meeting is to gather specialists from
different branches of mechanics to provide a platform for cross-fertilisation
of ideas.
HISTORY OF THE SCHOOL
The first Summer School was organized by Ya.G. Panovko and his colleagues in
1971. In the early years the main focus of the School was on nonlinear
oscillations of mechanical systems with a finite number of degrees of freedom.
The School specialized in this way because at that time in Russia (USSR) there
were held regular National Meetings on Theoretical and Applied Mechanics, and
also there were many conferences on mechanics with a more particular
specialization. After 1985 many conferences and schools on mechanics in
Russia were terminated due to financial problems. In 1994 the Institute for
Problems in Mechanical Engineering of the Russian Academy of Sciences
restarted the Summer School. The traditional name of "Summer School" has been
kept, but the topics covered by the School have been much widened, and the
School has been transformed into an international conference. The topics of
the School cover now all fields of mechanics and associated into
interdisciplinary problems.
SCIENTIFIC COMMITTEE (changes are possible)
* A.K. Abramian (IPME RAS, St. Petersburg, Russia)
* V.V. Beletsky (Space Research Institute, Moscow, Russia)
* I.I. Blekhman (IPME RAS, Mechanobr Research Institute, St. Petersburg,
Russia)
* M. Cartmell (University of Glasgow, UK)
* Y. Fu (University of Keele, UK)
* S.N. Gavrilov (IPME RAS, St. Petersburg, Russia)
* I.G. Goryacheva (Institute for Problems in Mechanics RAS, Moscow, Russia)
* E.F. Grekova (IPME RAS, St. Petersburg, Russia)
* D. Harris (UMIST, Manchester, UK)
* A.B. Freidin (IPME RAS, St. Petersburg, Russia)
* D.A. Indeitsev (IPME RAS, St. Petersburg, Russia) -- Co-Chairman
* E.A. Ivanova (IPME RAS, St. Petersburg State Technical University, Russia)
* A.M. Krivtsov (IPME RAS, St. Petersburg State Technical University, Russia)
* G.A. Leonov (IPME RAS, St. Petersburg State University, Russia)
* E.V. Lomakin (Moscow State Lomonosov University, Russia)
* G.A. Maugin (University of P. et M. Curie, Paris, France)
* N.F. Morozov (IPME RAS, St. Petersburg State University, Russia)
* R.W. Ogden (University of Glasgow, UK)
* V.A. Palmov (St. Petersburg State Technical University, Russia) --
Co-Chairman
* M. Wiercigroch (University of Aberdeen, UK)
* P.A. Zhilin (IPME RAS, St. Petersburg State Technical University, Russia)
* F. Ziegler (Technical University of Wien, Austria)
LOCAL ORGANIZING COMMITTEE
* A.D. Firsova, IPME RAS
* S.N. Gavrilov, IPME RAS
* E.F. Grekova, IPME RAS - Scientific Secretary
* A.D. Sergeyev, IPME RAS
* E.V. Serogo, IPME RAS
* E.V. Shishkina, IPME RAS
SCIENTIFIC PROGRAM
Presentations devoted to fundamental aspects of mechanics, or spreading the
field of applications of mechanics, are invited. We are particularly keen to
receive contributions that SHOW NEW EFFECTS AND PHENOMENA OR DEVELOP NEW
MATHEMATICAL MODELS. The topics of the School cover all fields of mechanics,
including, but NOT RESTRICTED, to
* mechanics of generalized continua (polar and micromorphic continua,
mixtures, porous media, electromagnetic continua, grains, powders etc)
* solids and structures
* phase transitions
* nanostructures and thin films
* wave motion
* nonlinear dynamics, chaos and vibration
* dynamics of rigid bodies and multibody dynamics
* fluid and gas
* computational mechanics
* mechanical and civil engineering applications
Four different forms of presentations are offered, namely, plenary lectures (1
hour), presentations at minisymposia (30 minutes), short communications (20
minutes), and posters. The working language is English. For the attention of
Russian participants: the Russian language as an exception can be used only in
posters, but even for posters English is strongly recommended. Regrettably we
can not provide simultaneous translation, and due to the international nature
of the School all the oral presentations must be in English.
Attention: each participant may only give ONE oral presentation.
The number of posters for each participant is not limited.
MINISYMPOSIA AND CHAIRS (preliminary information)
* Instabilities, Waves, and Phase Transitions in Nonlinear Elasticity
R.W. Ogden (Glasgow, UK), A.B. Freidin (St. Petersburg, Russia),
and Y. Fu (Keele, UK)
* Nonlinear Dynamics of Engineering Systems
E.E. Pavlovskaia, M. Wiercigroch (Aberdeen, UK)
* Nonlinear Strain Waves in Complex Deformable Solids
G.A. Maugin (Paris, France),
A.V. Porubov, A.M. Samsonov (St.Petersburg, Russia)
* Problems in the Mechanics of Granular Materials and Systems
D. Harris (Manchester, UK)
* Recent Advances in Random Vibrations
D. Iourtchenko (Miami, USA)
* Vibrational Mechanics and Synchronization
I.I. Blekhman (St. Petersburg, Russia)
Speakers include (to be completed):
Prof. E.L. Aero (St.Petersburg, Russia)
Acad. V.V. Beletsky (Moscow, Russia)
http://www.iki.rssi.ru/eng/people/beletsky_res.htm
Prof. I.I. Blekhman (St. Petersburg, Russia)
http://www.ipme.ru/ipme/labs/vm/index.htm
Prof. G. Capriz (Pisa, Italy) - to be confirmed
Dr. D. Harris (Manchester, UK)
http://www.ma.umist.ac.uk/dh/index.htm
Prof. Y. Fu (Keele, UK)
http://www.keele.ac.uk/depts/ma/people/yf/
Acad. I.G. Goryacheva (Moscow, Russia)
http://hp.iitp.ru/win/38/3883.htm
Prof. D.A. Indeitsev (St. Petersburg, Russia)
http://www.ipme.ru/ipme/labs/he/ind.htm
Prof. E.V. Lomakin (Moscow, Russia)
Prof. G.A. Maugin (Paris, France)
http://www.lmm.jussieu.fr/MEMBRES/MAUGIN/directeur.html
Acad. N.F. Morozov (St. Petersburg, Russia)
http://www.math.spbu.ru/user/morozov/
Prof. R.W. Ogden (Glasgow, UK)
http://www.maths.gla.ac.uk/~rwo/
Prof. V.A. Palmov (St. Petersburg, Russia)
http://www.unilib.neva.ru/stu/face_13.html
Prof. M. Wiercigroch (Aberdeen, UK)
http://wwwcad.eng.abdn.ac.uk/~eng373
Prof. P. Zhilin (St. Petersburg, Russia)
ORGANIZATIONAL DETAILS AND IMPORTANT DATES
Details concerning abstract submission and other organizational details are
available at our website
http://www.eng.abdn.ac.uk/~apm/2003
DATES TO REMEMBER:
* Application for financial support for young scientists from Russia
(abstract and registration form are required): January 15, 2003.
* Abstract submission: February 1, 2003.
* Submission of a visa form
(required to issue the invitation to Russia): February 1, 2003.
* Notification of acceptance: March 15, 2003.
* Paper submission (for plenary lectures, minisymposia and invited papers):
June 23, 2003.
* Conference: June 23-July 2, 2003.
REGISTRATION FEE
The conference fee is:
* for foreign participants giving a presentation: $250
* for foreign participants not giving a presentation: $190
* for foreign students: $190
The fee covers invitation costs, postage, book of abstracts, proceedings,
social program (excursion, get-together party), and organizational costs.
* The fee for foreign accompanying persons is $90 and covers the invitation
costs, postage, and social program.
* There is a reduced conference fee of $20 for participants from NIS countries
(Armenia, Azerbaijan, Belarus, Georgia, Kazakhstan, Kyrgystan, Moldova,
Russia, Tajikistan, Turkmenistan, Ukraine, Uzbekistan), which partially
covers the postage and book of abstracts.
The Organizing Committee is willing to apply for financial support for young
(not over 35 years old) scientists from Russia. To make an application,
please fill item 16 in the registration form, and send us BOTH
your registration form and your abstract before January 15, 2003.
For the attention of young participants from NIS countries: for the time being
we do not see a possibility to apply for financial support for you, since
INTAS has not announced this competition yet. If it does, we will make
an application, so just in case please mention your age on the registration
form if you wish to apply. Please look our website for up-to-date
information.
We regret that due to financial problems (we have only a limited support from
Russian organizations) we can not cover any expenses of our foreign
participants. However, we shall be glad to be of any help in making
(joint) applications for support, to provide any necessary letters etc.
If you have any comments or questions on this matter, we shall
be very pleased to hear from you.
CONFERENCE SITE
It is planned to hold the School in a suburb of St. Petersburg. The exact
location will be determined later. Please look at our website for up-to-date
information.
ST. PETERSBURG
St. Petersburg is going to celebrate its 300th birthday on May 27, 2003.
Many events and summits are planned for this occasion, and it will be very
difficult to get the tickets and obtain visa. So please, make your travel
plans in advance and follow the deadlines for visa information submission.
In June St. Petersburg has nice warm weather and the famous
white nights can be experienced. St. Petersburg is called the "Venice of the
North", since it is located among numerous rivers and channels of the delta of
the Neva river. St. Petersburg is in fact the "cultural capital" of Russia.
The magnificent Hermitage and Russian Museum give a flavour of the cultural
image of the city, where numerous theatres and the famous Russian ballet can
be found. For those more inclined towards nature, the Russian czars'
residences, for example Pavlovsk, Peterhoff, and Pushkin, can offer a pleasant
visit; or alternatively one can take an unforgettable boat trip through river
Neva and the city channels.
=================================================================
== APM'2003 ==
== Institute of Problems of Mechanical Engineering ==
== of Russian Academy of Sciences ==
== Bolshoy pr. V.O., 61, St.Petersburg, 199178, Russia ==
== Phone: +7(812)-3214772; ==
== Fax : +7(812)-3214771 ==
== http://www.eng.abdn.ac.uk/~apm/2003 ==
== E-mail: apm [at] eng [dot] abdn.ac.uk ==
=================================================================
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Date: Sat, 23 Nov 2002 18:32:19 -0700 (MST)
From: Vladik Kreinovich
Reply-To: Vladik Kreinovich
Subject: preliminary information: a meeting in SpB back-to-back with Denmark interval workshop
To: reliable_computing [at] interval [dot] louisiana.edu
Cc: kunin [at] uh [dot] edu, sstarks [at] utep [dot] edu, hunguyen [at] nmsu [dot] edu, vladik [at] cs [dot] utep.edu
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Dear Friends,
Several US folks have expressed preliminary interest in going to St.
Petersburg, Russia, after the PARA'04 Workshop on State-of-the-Art in
Scientific Computing in Lyngby, Denmark, June 20-23, 2004
http://lawra.uni-c.dk/para04/, a workshop at which Kaj Madsen, one of the
workshop's organizers, plans to have a strong interval presence.
My colleague Isaak Kunin informed me that every year, at the end of
June-beginning of July, there is a Summer School "Advanced Problems in
Mechanics" (mechanics understood in most general sense) that encourages various
talks, interval methods are welcome. If there is enough interest, we can have a
special session there. They usually meet in Repino a nice suburb of St.
Petersburg.
Alternatively, if Slava and other SpB folks want to organize something that is
also a possibility.
If there are only a few folks we can simply have a few talks in SpB and spend
time talking to each other and to Slava and others and touring the city :-)
Let me know if you are potentially interested.
Vladik
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Date: Mon, 25 Nov 2002 14:07:59 +0100
From: Arnold Neumaier
Organization: University of Vienna
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To: Stefan Ratschan ,
"Schichl, Hermann"
CC: reliable_computing [at] interval [dot] louisiana.edu
Subject: Re: Solutions of systems of equations
References: <200211181105.gAIB5Rg29319 [at] contact [dot] mpi-sb.mpg.de>
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On Mon, 18 Nov 2002 12:05, Stefan Ratschan wrote:
>
> I could not find a single algorithm
> for which it is proven that it does the following:
>
> Input:
> A system of non-linear equations F=0, and
> a box B
> Output:
> (1) Yes, if F=0 contains a zero in B that does not vanish under perturbations,
> (2) no, if F=0 does not contain zeros in B.
> Otherwise
> (3) (there are some zeros in B, but all of them vanish under
> perturbations), the algorithm does not terminate.
>
> Of course the zeros might be arbitrarily ill-conditioned. However,
> this just requires the use of arbitrarily high floating-point
> precision.
I think that the algorithm on p.211 of my book 'Interval methods
for Systems of Equations' can be modified to have this property.
Only Step 3 must be modified, as follows:
Instead of printing 'x possibly contains a solution',
double the precision of the arithmetic in the current box
(and all its subboxes) and continue with Step 4 (instead of Step 6).
And after using the methods of Section 5.5 to verify
a solution, if they fail, also use the topological degree methods
of Kearfott and Dian. The precision then controls decisions made
in Step 2.
For if an isolated zero is stable under arbitrary small perturbations
(which has to be made precise in a suitable way for the question
to be meaningful), the degree must be nonzero, and this can be verified
with interval arithmetic over sufficiently small boxes.
While I have no immediate proof of this, I think it should be
not difficult to prove.
And if there is a manifold of zeros, I believe that (by versions
of Sard's Lemma) it is not stable under small (but sufficiently
general) perturbations (assuming the system is n by n).
The real difficulties are with problems that are unstable under
arbitrary perturbations, but where not all perturbations are
natural. For example, for problems in which all coefficients are
integers, one would like to have an algorithm that makes the
decision between (1) and (2) without running forever. This may
bring the halting problem into play, as Hermann mentioned.
Thus to make the question precise and interesting, one must
carefully define not only which class of equaltions but also
which class of perturbations are to be allowed.
Computationally most relevant is the case where one wants to
solve F(x,c)=0, dim x = dim F, where F is defined as a vector of
arithmetic expressions in x and c with integer coefficients
(assumed to be exact) and the only permitted perturbations are
those of the coefficient vector c. To make the problem generic,
one would have to require that for each fixed x,c, the set of
F(x,c+eps), with a vector eps in a small neighborhood of zero,
has positive measure, or perhaps (which is much easier) contains
zero in its interior.
Arnold Neumaier
From owner-reliable_computing [at] interval [dot] louisiana.edu Mon Nov 25 14:23:43 2002
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Date: Mon, 25 Nov 2002 13:23:24 -0700 (MST)
From: Vladik Kreinovich
Reply-To: Vladik Kreinovich
Subject: 1st announcement JAF 22
To: reliable_computing [at] interval [dot] louisiana.edu
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------------- Begin Forwarded Message -------------
Date: Fri, 01 Jan 1904 07:20:02 +0100
Subject: 1st announcement JAF 22
From: "Paola D'Aquino"
Call for participation
International meeting "22nd Journ=E9es sur les Arithm=E9tiq=
ues
Faibles "
June 11-14, 2003
Napoli, Italy
MAIN TOPICS
For a detailed description of what are "Weak Arithmetics" visit
http://www.univ-paris12.fr/lacl/jaf/html/wa.html
The meeting will cover traditional topics of the "Days" such as:
Provability in weak arithmetics
Definability in weak arithmetics
Weak arithmetics and model theory
Decidability/undecidability of weak logical theories
Modelling computations in the frameworks of weak arithmetics
Besides them a special session in general algebra will be organized on
11 June
PERMANENT COMMITTEE of the DAYS:
Patrick CEGIELSKI Jean-Pierre RESSAYRE Denis RICHARD
University Paris-12 CNRS, Jussieu University of Auvergne
Fontainebleau IUT Clermont IUT, LLAIC1
PROGRAM COMMITTEE
Patrick CEGIELSKI (France)
Paola D'AQUINO (Italy)
Ulderico DARDANO (Italy)
Jean-Pierre RESSAYRE (France)
Denis RICHARD (France)
Local ORGANIZING COMMITTEE :
Paola D'AQUINO (Seconda Universita=B9 di Napoli)
Ulderico DARDANO (Universita=B9 di Napoli =B3Federico II=B2
Andrea Vietri (Universita=B9 di Roma =B3La Sapienza=B2)
Working LANGUAGE: English
SUBMISSION of papers
To this goal the facilities of Atlas Mathematical Conference Abstracts
will be used. In the second announcement you will receive instructions.
The deadline for submission is 31 March 2003
REGISTRATION
Please fill in the attached word file with your details and send it to
dardano [at] unina [dot] it
PARTECIPATION FEE:
There is a partecipation fee of 80 euros to be paid on arrival. This will
cover coffee breaks, information material, social dinner.
PLACE of the meeting:
The "22nd JAF" will be held at the Istituto per gli Studi Filosofici
which is situated in via Monte di Dio, Napoli
ACCOMODATION
There are many hotels inthe area nearby Istituto per gli Studi
Filosofici, which is right in the city center of Napoli. In the second
announcement you will find a list of hotels with prices and we recommend
that you book the hotel you prefer by yourself. The majority of hotels
accept a fax with your visa number
VISAS
Those who need a visa should write to paola.daquino [at] unina2 [dot] it
and fill in the details in the registration form.
CONTACTS
For more information on the meeting please contact paola.daquino [at] unina2 [dot] it
------------- End Forwarded Message -------------
--Cast_of_Falcons_451_000
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--Cast_of_Falcons_451_000--
From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Nov 26 12:22:48 2002
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From: Stefan Ratschan
To: reliable_computing [at] interval [dot] louisiana.edu
In-reply-to: <3DE220AF.9B5063C5 [at] univie [dot] ac.at> (message from Arnold Neumaier on
Mon, 25 Nov 2002 14:07:59 +0100)
Subject: Re: Solutions of systems of equations
References: <200211181105.gAIB5Rg29319 [at] contact [dot] mpi-sb.mpg.de> <3DE220AF.9B5063C5 [at] univie [dot] ac.at>
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Dear colleagues,
thanks a lot for the very helpful answers to my question. This is
really the MOST USEFUL scientific mailing list I have found so far.
> I think that the algorithm on p.211 of my book 'Interval methods
> for Systems of Equations' can be modified to have this property.
> Only Step 3 must be modified, as follows:
> Instead of printing 'x possibly contains a solution',
> double the precision of the arithmetic in the current box
> (and all its subboxes) and continue with Step 4 (instead of Step 6).
The problem is that bisection might put a box border directly onto a
root, and then one cannot even verify existence within the created
boxes using multiprecision floating-point arithmetic. Probably this is
why step 3 then tries to do verification on a "narrow
superbox". Unfortunately this is a little bit vague.
A possibility to deal with this would be epsilon-inflation (from the
midpoint of the box, or from the result of a local search).
Unfortunately I could not find much proving the success of this method
("G. Mayer: Epsilon-inflation in verification algorithms; J. of Comp. and
Appl. Math. 1995" proves things only in a restricted setting).
Are there any general results about the success of epsilon-inflation?
Or is there an alternative way of dealing with this problem?
Again many thanks for the helpful answers,
Stefan
From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Nov 26 13:03:55 2002
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Date: Tue, 26 Nov 2002 13:03:33 -0600
To: Stefan Ratschan ,
reliable_computing [at] interval [dot] louisiana.edu
From: "R. Baker Kearfott"
Subject: Re: Solutions of systems of equations
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Stefan,
There are a number of general results in the literature. Arnold
Neumaier's book is one source.
I studied, in a fairly elementary setting, conditions under which
an interval Newton method will succeed in existence (or uniqueness)
verification in my book (Rigorous Global Search -- Continuous
Problems, Kluwer, 1996), section 6.2.2. In particular, look at the bottom
of page 222.
Best regards,
Baker
At 07:22 PM 11/26/2002 +0100, Stefan Ratschan wrote:
>
>A possibility to deal with this would be epsilon-inflation (from the
>midpoint of the box, or from the result of a local search).
>Unfortunately I could not find much proving the success of this method
>("G. Mayer: Epsilon-inflation in verification algorithms; J. of Comp. and
>Appl. Math. 1995" proves things only in a restricted setting).
>
>Are there any general results about the success of epsilon-inflation?
>Or is there an alternative way of dealing with this problem?
>
>Again many thanks for the helpful answers,
>
> Stefan
>
>
---------------------------------------------------------------
R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax)
(337) 482-5270 (work) (337) 981-9744 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------
From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Nov 26 22:13:12 2002
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Date: Tue, 26 Nov 2002 21:12:44 -0700 (MST)
From: Vladik Kreinovich
Reply-To: Vladik Kreinovich
Subject: NAFIPS update
To: reliable_computing [at] interval [dot] louisiana.edu
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FYI. North American Fuzzy Information Processing Society NAFIPS traditioonally
wecomes both individual interval talks and interval sessions.
------------- Begin Forwarded Message -------------
From: Michael Berthold
Date: Mon, 25 Nov 2002 21:18:55 -0800 (PST)
To: vladik [at] cs [dot] utep.edu
Subject: NAFIPS update
...
I hope that you will consider
attending NAFIPS-2003 in Chicago on July 24-26. Abstracts
are due soon, so please check the website (www.nafips2003.org)
for information on the conference.
While you are checking your calender, NAFIPS 2004 will be held
in beautiful Banff (Alberta, Canada) on June 27-30, 2004. Make
your plans early--this is an excellent opportunity to combine
coming to NAFIPS with a trip to the Rocky Mountains!
Thank you for your past participation in NAFIPS and we look forward
to another year of serving the fuzzy set and soft computing community.
Best Regards,
Michael Berthold
(President, NAFIPS)
------------- End Forwarded Message -------------
From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Nov 27 02:45:16 2002
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Date: Wed, 27 Nov 2002 19:44:48 +1100 (EST)
From: Richard Smith - Systems Engineer - Melbourne
Reply-To: Richard Smith - Systems Engineer - Melbourne
Subject: Re: Solutions of systems of equations
To: reliable_computing [at] interval [dot] louisiana.edu
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Reading through the original problem and subsequent responses left me just
a bit uneasy. It seemed that the original statement exposes the limits of
computing with sets. We may be able to shrink these sets, but not indefinitely
given finite precision. Algorithms that apply contractive mappings and stop
when the set no longer shrinks will terminate in finite time, but possibly
leave unanswered the question re existence of a [single] zero.
However if we can assume [or know apriori] continuity and differentiability then
we might be able to make stronger statements, with the strength of a theorem,
about a [small] box/region/subpaving/set.
In some sense I think of interval arithmetic as being like probing atomic
structure with [high-energy] particles displaying wave-like behaviour. This
places fundamental limits on the ability to explore a region of space. Sure,
use higher energy particles [greater precision], but run into the same limit.
What does the solution to a set of non-linear equations really "look like"?
And with finite precision, what is the smallest possible collection of
subpavings that enclose the solution set? I imagine a whole string of boxes
possibly 1 ULP wide. Without further knowledge about properties so as to
invoke Mean Value Theorem, where next?
============================================================================
,-_|\ Richard Smith - SE Melbourne
/ \ Sun Microsystems Australia Phone : +61 3 9869 6200
richard.smith [at] Sun [dot] COM Direct : +61 3 9869 6224
\_,-._/ 476 St Kilda Road Fax : +61 3 9869 6290
v Melbourne Vic 3004 Australia
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Date: Thu, 28 Nov 2002 11:01:09 -0700 (MST)
From: Vladik Kreinovich
Reply-To: Vladik Kreinovich
Subject: conference of potential interest to interval researchers
To: reliable_computing [at] interval [dot] louisiana.edu
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From: Gravvanis George
To:
Cc: Gravvanis George
Subject: [CFP] MINI_SYMPOSIUM / HERCMA 2003
Date: Wed, 27 Nov 2002 22:55:08 +0200
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C A L L F O R P A P E R S
=================================
FOR THE MINI-SYMPOSIUM ON
PRECONDITIONING AND ITS APPLICATIONS
Mini-Symposium Organizer: Dr. G. A. Gravvanis
Within the framework of the Conference
======================================
H E R C M A 2003
The Sixth Hellenic European Research on Computer Mathematics and its
Applications
September 25-27, 2003, Athens University of Economics and Business,
Athens, Greece
Topics of the session: Topics of interest include, but no limited to, the
following: Approximate Inverses, Finite Difference and Finite Element
method, Finite Volume method, Boundary element method, Domain
Decomposition methods, Multigrid Methods, Parallel iterative methods,
Numerical Software Description and Environments, Advanced Numerical
Algorithms and Scientific Computing, Applications in Science and
Engineering.
Prospective authors are invited to submit an extended two-page abstract by
20th February 2003 on topics related to the theme of the Session (PDF,
Postscript, or Microsoft Word documents) to the Session Organizer by email
only (gag [at] aegean [dot] gr )
The extended abstract, not over 2-typed A4-pages with 1.5 spacing,
including figures and diagrams may include the general significance of the
original research work as well as the detailed aspects of the study that
is going to be presented. All communications must be in English and bear
the names of all authors, their affiliations and full mailing addresses.
Recommendations concerning the format of the accepted paper to be
published in the HERCMA Conference Proceedings will be sent to authors.
Papers must not have been previously published or currently submitted for
publication elsewhere.
Soon after the Conference, extended forms of selected papers will be
considered for the HERMIS-ìð special issue publication and other journals
publication.
IMPORTANT DATES:
February 20, 2003: Deadline for the submission of the extended abstract
April 10, 2003: Notification of acceptance
May 30, 2003: Deadline for the submission of the complete paper
(camera ready)
September 25-27, 2003: Sixth HERCMA Conference
SESSION CONTACT:
Dr. George A. Gravvanis
Department of Information and Communication Systems Engineering
University of the Aegean
GR-83200 Karlovasi, Samos, GREECE
E-mail: gag [at] aegean [dot] gr
Telephone: +30-2273-082230, +30-21-03368024, Fax: +30-2273-082009.
For more information about the conference a link has been created at
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Fri, 29 Nov 2002 12:36:46 +0100
From: Norbert Mueller
To: cca-list@fernuni-hagen.de, reliable_computing [at] interval [dot] louisiana.edu,
comprox [at] doc [dot] ic.ac.uk, communaute [at] medicis [dot] polytechnique.fr,
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Subject: CfP - special issue of JLAP: exact real number computation
Date: Fri, 29 Nov 2002 12:36:45 +0100
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---------------------Third (and last) call for papers--------------------=
---
The
Journal of Logic and Algebraic Programming
is preparing a=20
Special issue on
the practical development of exact real number computation.
You may find the Call for Papers at:
http://www.informatik.uni-trier.de/~mueller/JLAP/
Attached please find the ASCII-Version of the CfP.
=20
Deadline for submissions: December 31, 2002.
------------------------------------------
I am sorry if you receive multiple copies!
------------------------------------------
Kind regards
--=20
Dr. Norbert Mueller
FB IV - Abteilung Informatik * Universitaet Trier * D-54286 Trier (Germ=
any)
email: mueller@uni-trier.de * http://www.informatik.uni-trier.de/~muel=
ler/
Tel: ..49-(0)651-201-2845/2848 * Fax: ..49-(0)651-201-3805
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------------------------------------------------------------------------
Journal of Logic and Algebraic Programming
Special issue on
the practical development of exact real number computation
Web Page: http://www.informatik.uni-trier.de/~mueller/JLAP
Deadline for submissions: December 31, 2002
------------------------------------------------------------------------
Exact real number computation addresses the gap between the practice and
theory of working with real numbers. On the practical side, floating
point numbers with fixed precision (being a finite set... ) dominate the
daily use of real numbers on computers. On the theoretical side, models
of computability and computational complexity in analysis have grown in
parallel. We seek to close the gap by e.g.
- research on programming languages for non denumerable data sets
- algorithms of approximate nature but with unrestricted precision
Here 'unrestricted precision' denotes the possibility to achieve results
with an arbitrary high precision, usually combined with a strict error
analysis or with the use of interval methods.
The Journal of Logic and Algebraic Programming is an international
journal whose aim is to publish original work in the areas of logical
and algebraic methods and techniques for programming in its broadest
sense.
The Journal of Logic and Algebraic Programming complements Elsevier's
Science of Computer Programming and Theoretical Computer Science by its
focus on the foundations of logical, algebraic and categorical methods
for programming.
For more information, visit http://www.elsevier.com/locate/jlap.
This special issue covers the spectrum from theoretical results to
concrete applications of exact real number computation, with an emphasis
on programming languages and implementations.
Submissions are sollicited on topics including, but not limited to:
- abstract models of computation for non denumerable sets
- programming languages for exact real arithmetic
- data structures for exact real numbers or for `large` subsets
of the reals
- algorithms for exact arithmetic on real numbers
- algorithms for approximate arithmetic or interval arithmetic,
but with unrestricted precision
- complexity theory related to arithmetic on real numbers
- symbolic or algebraic computations on real numbers
- survey articles or case studies on the area
We look for original, unpublished contributions of high quality that are
not submitted elsewhere. All submissions will be evaluated on the the
ususal criteria (like technical content, originality... ), but also on
how they "bridge the gap", i.e. having both theoretical aspects and
practical experiments will be a bonus.
Deadline for submissions is December 31, 2002.
Authors will be notified of acceptance or rejection before May 1, 2003.
We anticipate publication of the special issue about end of 2003.
Authors are requested to submit their paper (in either Postscript or PDF)
electronically to the chief editor indicated below. We encourage the use
of the Elsevier style file with LaTeX
(see http://www.elsevier.com/locate/latex).
In order to speed up the review process, authors are strongly encouraged
to send (tentative) title and abstract to the chief editor as soon as
available.
Chief editor:
Norbert Mueller mueller@uni-trier.de
Fachbereich IV - Abteilung Informatik
Universitaet Trier
D-54286 Trier
Germany
Guest editors:
Martin Escardo m.escardo [at] cs [dot] bham.ac.uk
School of Computer Science
University of Birmingham
Birmingham B15 2TT
England
Paul Zimmermann Paul.Zimmermann [at] loria [dot] fr
INRIA Lorraine
Technopole de Nancy-Brabois
615 rue du Jardin Botanique, BP 101
F-54600 Villers-les-Nancy
France
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