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dear all,
I am a new comer in INTERVAL arithmetic. Suppose there are two INTERVAL
variables X1 and X2, I want to make a logical comparison to know if X1 is in X2
or some kind of overlapping. Is there any algorithm or library on this
operation?
Thanks
Haitao Huang
IC UK
From ownerreliable_computing [at] interval [dot] usl.edu Wed Jul 7 11:15:05 1999
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Date: Wed, 07 Jul 1999 11:15:22 0500
To: h.haitao [at] ic [dot] ac.uk
From: "R. Baker Kearfott"
Subject: Re: comparison of two intervals
Cc: reliable_computing [at] interval [dot] usl.edu
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Haitao,
There are various systems. In our Fortran 90 module INTERVAL_ARITHMETIC
(and in our package GlobSol), and in most elementary treatments of
interval arithmetic, you have the operations of "subset" and "disjoint".
Bill Walster et al at Sun Microsystems (Bill.Walster [at] Eng [dot] Sun.COM) have
devised a richer set of operators to make various logical situations
easier to implement. These operators are available with the GNU f77
intervalenhanced compiler (ask Prof. Mike Schulte at
schulte [at] eecs [dot] lehigh.edu). In this system, X1 is "certainly equal" to
X2 if X1 and X2 are the same point; X1 is "possibly equal" to X2 if
X1 and X2 overlap, and X1 and X2 are equal as sets if they are the
same intervals. (Similarly, you have "possibly not equal", "certainly
not equal" and "not equal as sets", etc.)
Best regards,
Baker
P.S. Of course, in a homegrown implementation, if you are representing
intervals using end points, you can compare the end points to get
the answers you want. But I'd recommend one of the prewritten
packages at this point, in Fortran, C, C++, Pascal, or Matlab.
At 03:42 PM 7/7/99 +0100, you wrote:
>dear all,
>
>I am a new comer in INTERVAL arithmetic. Suppose there are two INTERVAL
>variables X1 and X2, I want to make a logical comparison to know if X1 is in X2
>or some kind of overlapping. Is there any algorithm or library on this
>operation?
>
>Thanks
>
>Haitao Huang
>IC UK
>
>

R. Baker Kearfott, rbk [at] usl [dot] edu (318) 4825346 (fax)
(318) 4825270 (work) (318) 9819744 (home)
URL: http://interval.usl.edu/kearfott.html
Department of Mathematics, University of Southwestern Louisiana
USL Box 41010, Lafayette, LA 705041010, USA

From ownerreliable_computing [at] interval [dot] usl.edu Wed Jul 7 11:23:07 1999
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Date: Wed, 7 Jul 1999 10:22:47 0600 (MDT)
From: vladik
ReplyTo: vladik
Subject: Re: Your Message Sent on Wed, 7 Jul 1999 15:42:52 +0100
To: reliable_computing [at] interval [dot] usl.edu, h.haitao [at] ic [dot] ac.uk
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> From: h.haitao [at] ic [dot] ac.uk
> Date: Wed, 7 Jul 1999 15:42:52 +0100
> To: reliable_computing [at] interval [dot] usl.edu
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>
> dear all,
>
> I am a new comer in INTERVAL arithmetic. Suppose there are two INTERVAL
> variables X1 and X2, I want to make a logical comparison to know if X1 is in
X2
> or some kind of overlapping. Is there any algorithm or library on this
> operation?
If I understand you correctly, you mean that:
* you have two intervals X1=[a1,b1] and X2=[a2,b2], and
* you want to check:
* whether X1 is a subset of X2, and
* whether X1 and X2 overlap (i.e., whether these two intervals have common
elements).
Both relations can be expressed in terms of simple inequalities between the
intervals' endpoints, so both checks can be done easily by comparing the
endpoints of the intervals X1 and X2:
* X1 is a subset of X2 if and only if a2<=a1 and b1<=b2
* the intervals X1 and X2 have a common element if and only if
max(a1,a2)<=min(b1,b2), i.e., iff a1<=b2 and a2<=b1.
Yours
Vladik
Vladik Kreinovich
Department of Computer Science
University of Texas at El Paso
El Paso, TX 79968
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From: "Bill Older"
To: h.haitao [at] ic [dot] ac.uk, reliable_computing [at] interval [dot] usl.edu
Subject: RE:
Date: Wed, 7 Jul 1999 14:21:23 0400
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Haitao,
This area was explored some in BNR Prolog's interval constraint system. In a
functional
interval package (where intervals are essentially just conventional data
structures),
a variety of such relations (Allen relations) can be defined of course.
However, in the constraint framework the possibilities are very restricted
because of the formal requirements of monotonciity and stability under
narrowing etc.
The subinterval relation X <= Y is one which can be defined and is both
interesting and useful.
Its interval (2nd order) interpretation is that X is contained in Y, with
the degenerate case of
X element of Y when X is a point, and the doubly degenerate 1st order
interpretation as equality.
As a constraint, however, it acts as a "diode", propagating narrowing from Y
to X and not from X to Y; it therefore plays a role similar in many ways to
assignment operators in conventional programming languages. In particular,
observational data can be gated through such a diode into an interval
computation so that the computation cannot backnarrow the data. Similarly,
the parameters of a parametrized computation can be isolated from the
computations they control and so on.
The other two relations I recall that are constraint defineable are "ends
together" = and "starts together" =. These allow if I remember
correctly  the relation of "overlaps" to be formulated as a constraint,
from which follows the nary relation "connected/covers". Note that these
examples are all different ways of splitting the equality relation, == is
equiv. <= & => and also == is equiv. = & =.
Bill Older
Original Message
From: h.haitao [at] ic [dot] ac.uk [mailto:h.haitao [at] ic [dot] ac.uk]
Sent: Wednesday, July 07, 1999 10:43 AM
To: reliable_computing [at] interval [dot] usl.edu
Subject:
dear all,
I am a new comer in INTERVAL arithmetic. Suppose there are two INTERVAL
variables X1 and X2, I want to make a logical comparison to know if X1 is in
X2
or some kind of overlapping. Is there any algorithm or library on this
operation?
Thanks
Haitao Huang
IC UK
From ownerreliable_computing [at] interval [dot] usl.edu Wed Jul 7 22:02:18 1999
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From: "George Corliss"
To:
Cc:
References: <22796.199907071442 [at] sunv6 [dot] ps.ic.ac.uk>
Subject: Re:
Date: Wed, 7 Jul 1999 22:02:03 0500
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Haitao and all,
> I am a new comer in INTERVAL arithmetic. Suppose there are two INTERVAL
> variables X1 and X2, I want to make a logical comparison to know if X1 is in
X2
> or some kind of overlapping. Is there any algorithm or library on this
> operation?
The responses circulated to your query have been added to my
interval FAQ site. See
http://www.mscs.mu.edu/~georgec/IFAQ/huang1.html
George F. Corliss
Dept. Math, Stat, Comp Sci
Marquette University
P.O. Box 1881
Milwaukee, WI 532011881 USA
georgec [at] mscs [dot] mu.edu; CorlissG [at] Marquette [dot] edu
http://www.mscs.mu.edu/~georgec/
Office: 4142886599; Dept: 2887375; Fax: 2885472
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>From scan98 Tue Jul 13 14:04:36 +0200 1999 remote from inf.uszeged.hu
Date: Tue, 13 Jul 1999 14:04:36 +0200 (MET DST)
From: SCAN98
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Subject: address changed for SCAN98
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Dear Colleagues,
due to technical reasons beyond my control, the internet address of the
SCAN98 conference has been changed to
http://www.inf.uszeged.hu/scan98
(a ~ was deleted in front of scan98). Please change the address if you
have it in a pointer on your web page.
Yours,
Tibor Csendes

SCAN98
IMACS/GAMM International Symposium on
Scientific Computing, Computer Arithmetic and Validated Numerics
September 22  25, 1998, Budapest, Hungary
Tel.: +36 62 454 305 Fax: +36 62 420 292
Email: scan98 [at] inf [dot] uszeged.hu http://www.inf.uszeged.hu/scan98
From ownerreliable_computing [at] interval [dot] usl.edu Wed Jul 14 19:07:32 1999
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From: "Chenyi Hu"
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Date: Wed, 14 Jul 1999 18:56:45 0700
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Subject: Interval BLAS
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Hello,
The public commenting period for the BLAST document is from
July 9 to August 31, 1999. Interval BLAS is the Chapter 5 of
the BLAST document. You are welcome to peruse the document and
make comments online at the URL:
http://www.netlib.org/blas/blastforum/blastforum.html
Attached is the message about the public commenting period
posted on NA Digest, V. 99, # 28 by Drs. Jack Dongarra and
Sven Hammarling.
Thanks for your attention!
Chenyi Hu

Ph.D., Associate Professor, Computer and Mathematical Sciences
Center for Computational Science and Advanced Distributed Simulation
University of HoustonDowntown Phone: 713 2218414
One Main Street Fax: 713 2218086
Houston, Texas 77002 Email: CHu [at] uh [dot] edu
http://happy.dt.uh.edu/~hu/Hu.html
attachment
From: Jack Dongarra
Date: Sat, 10 Jul 1999 07:33:46 +0200
Subject: Public Commenting Period for the BLAST document
Public Commenting Period for the BLAST document
July 9  August 31, 1999
During a series of meetings of the BLAS Technical Forum, we have
drafted a "BLAST document".
http://www.netlib.org/blas/blastforum/blastforum.html
The Forum was established to consider expanding the Basic Linear
Algebra Subprograms (BLAS) in a number of directions in the light of
modern software, language, and hardware developments.
The resulting document is now available for public comments. Wide input
is needed to help ensure that emerging proposals are useful and acceptable
to the community.
After this "public commenting period" from July 9 to August 31, we will
have a final "virtual meeting" (September 1  September 30) of the Forum
to incorporate comments and perform final voting on the chapters.
And on October 1, the publication of the BLAST document (like MPI
report, freely available in electronic form) will occur.
For more information see:
http://www.netlib.org/blas/blastforum/blastforum.html
Jack Dongarra and Sven Hammarling


Ph.D., Associate Professor, Computer and Mathematical Sciences
Center for Computational Science and Advanced Distributed Simulation
University of HoustonDowntown Phone: 713 2218414
One Main Street Fax: 713 2218086
Houston, Texas 77002 Email: CHu [at] uh [dot] edu
http://happy.dt.uh.edu/~hu/Hu.html
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Announcement of a Ph. D. thesis
A Ph. D. Thesis of Mrs. Christiane Sonnenschein who was
one of my students, came out. The title is
"Zur Minimierung nichtdifferenzierbarer programmierbarer Funktionen"
(be aware, it is in German).
An electronic version of the thesis,
which deals with interval arithmetic nonsmooth optimization
can be found in her homepage
www.dpc.de/Journal/Diss/homediss.html
which also contains an English summary.
You also can send her a message under
csonnen [at] dpc [dot] de
Helmut Ratschek
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From: "Siegfried M. Rump"
To: "'reliable_computing'"
Subject: LAA special issue
Date: Sat, 17 Jul 1999 17:53:30 +200
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Dear colleagues:
we already received a number of papers for the special issue
of LAA on selfvalidating methods, and a number of papers
are promised.
This is again to remind and encourage submission  if it is
not already on your agenda. Remember the range of suitable
papers is large (see below), including nonlinear or differential
equations as long as there is some kind of linearization in it
(which, I guess, is almost always the case).
As you know, deadline for submission is September 30, 1999.
We sincerely hope for a good special issue  a good chance
to generate public attention to our field.
With best regards and best wishes,
Siegfried M. Rump
===============================================
Linear Algebra and its Applications (LAA)
Special issue on
LINEAR ALGEBRA IN SELFVALIDATING METHODS .
The goal of selfvalidating methods is to compute correct results on
digital computers  correct in a mathematical sense, covering all
errors like representation, discretization, rounding errors or others.
These methods have a connection to linear algebra since problems are
frequently transformed into linearized problems with uncertain data.
Then the linearization and discretization errors are estimated, possibly
together with an infinite dimensional part of the problem.
It has turned out that computation of an inclusion of the solution complex
of even a linear system of equations with uncertain data is NPhard. This
has given rise to interesting connections between selfvalidating methods
and complexity theory. Despite this, in many cases a reasonably sharp
inclusion can be calculated. The class of problems being solvable in this
sense has been extended in recent years.
The possibility to estimate the range of a function is a main ingredient
of selfvalidating methods. Beside the naive way to get error bounds by
replacing every operation by the corresponding interval operation, much
more elaborate methods have come up using gradients, slopes,
lp and qpapproaches and more.
In the past few decades the area of selfvalidating methods has been
evolving, with rapidly growing number of researchers. We want to
take this opportunity to publish a special issue on selfvalidating
methods. A preliminary list of topics would include:
 systems of linear equations and inequalities
 range of functions
 complexity theory for problems with uncertain data
 componentwise distance to singularity and/or stability
 sparse systems of equations
 algebraic eigenvalue problems
 iterative methods
 matrix methods in validation methods for differential
equations
 use of Mmatrices and Hmatrices in validation methods
 analysis of zeros and connection to controllability
 combination of computer algebra with floating point methods.
This is a sample, but not an exclusive list of topics. If there is
doubt about suitability of a particular paper, contact one of the
editors of the special issue.
Please submit three (3) hard copies to one of the special issue editors
listed below. The deadline for submission is SEPTEMBER 30, 1999.
Jiri Rohn
Faculty of Mathematics and Physics
Charles University
Malostranske nam. 25
118 00 Prague
Czech Republic
email: rohn [at] uivt [dot] cas.cz
Siegfried M. Rump
Inst. f. Computer Science III
Technical University HamburgHarburg
Schwarzenbergstr. 95
21071 Hamburg, Germany
email: rump@tuharburg.de
Tetsuro Yamamoto
Department of Mathematics
Faculty of Science
Ehime University
Matsuyama 790, Japan
email: yamamoto [at] dpc [dot] ehimeu.ac.jp
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From: Marc.Giusti [at] medicis [dot] polytechnique.fr (Marc Giusti)
MessageId: <199907231510.RAA25219 [at] marie [dot] medicis.polytechnique.fr>
Subject: computer algebra center MEDICIS
To: giusti [at] marie [dot] medicis.polytechnique.fr (Marc Giusti)
Date: Fri, 23 Jul 1999 17:10:21 +0200 (MET DST)
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Dear Colleague,
Sorry for possible multiple annoucements.
Through the presentation below, I invite you to discover the resources
of the Computer Algebra Center MEDICIS, under the supervision of CNRS
and Ecole polytechnique.
Regards,
Marc Giusti
Director of UMS MEDICIS

(you will find again this text on the Web ** with all associated links ** at
http://www.medicis.polytechnique.fr/medicis/crieng.html)

MEDICIS: What is it ? and how can I gain access ?
MEDICIS is a french "Unite Mixte de Service" and is part
of CNRS and the Ecole polytechnique.
It's role is a centre of resources for computer algebra.

It can be used by anybody to solve scientific calculations with the tools of
computer algebra and symbolic computation. It can, in effect, put at your
disposal hardware resources, software and expertise.
[+] In this way, MEDICIS can respond to your needs e.g.:
* a need for a large central memory
> 2 machines in the cluster having 2 Gb of memory.
* a need for a 64bits architecture
> 8 Alpha500 Mhz processors.
* a need for parallel calculus
> 16 Pentium II400 Mhz processors.
* a need for computer algebra software
> the current list which can be completed with your demands.
* a need for contacts with knowledgeable users of computer algebra
> already more than 200 users.
In total, there are
 approximately 13 Ghz of CPU
 11 Gb of central memory
 12 up to date large software packages of computer algebra
 a local 100 Mbs switched and secure network
 a systemnetworkapplications administrator
 200 experts and knowledgeable users,
who are available at your disposal.
[+] To find out more or to gain access, we invite you to read:
* a detailed presentation on the centre of resources MEDICIS ;
* the scientific requirements for gaining access ;
* in concrete terms, how to get an account and use it ;
* and finally the WEB server of MEDICIS, particularly the activities of
MEDICIS.
From ownerreliable_computing [at] interval [dot] usl.edu Wed Jul 28 03:52:09 1999
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Date: Wed, 28 Jul 1999 03:53:27 0500
To: reliable_computing [at] interval [dot] usl.edu
From: "R. Baker Kearfott"
Subject: New version of GlobSol
Sender: ownerreliable_computing [at] interval [dot] usl.edu
Precedence: bulk
Colleagues,
I have just uploaded a new version of our GlobSol global optimization
package. Some changes are:
(1) The installation process has been further simplified, and the read.me
(with instructions) has been clarified.
(2) GlobSol has been restructured so the overall search is now callable as
a subroutine.
(3) Capability for having "constants" that can be changed during the
optimization process has been introduced.
(4) Several bugs have been fixed.
(5) The configuration file(s) has been simplified.
See the revised downloading instructions at
http://interval.usl.edu/GlobSol/download_GlobSol.html
for further details.
See the GlobSol home page at
http://www.mscs.mu.edu/~globsol/
and, in particular, browse the Draft User Guide (available from the GlobSol
home page) for an explanation of GlobSol.
I have run integration tests with each of the four compiler / OS versions
I support. (I also provide instructions for modifying the makefile for
other compiler / OS combinations.) Please contact me with any problems.

I also wish to point out a new preprint, "On Stopping Criteria in Verified
Nonlinear Systems or Optimization Algorithms" that is available in
Postscript or DVI by clicking on the appropriate place in my preprints
page at
http://interval.usl.edu/preprints.html
Best regards,
Baker

R. Baker Kearfott, rbk [at] usl [dot] edu (318) 4825346 (fax)
(318) 4825270 (work) (318) 9819744 (home)
URL: http://interval.usl.edu/kearfott.html
Department of Mathematics, University of Southwestern Louisiana
USL Box 41010, Lafayette, LA 705041010, USA

From ownerreliable_computing [at] interval [dot] usl.edu Wed Jul 28 10:55:02 1999
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Date: Wed, 28 Jul 1999 08:54:33 0700 (PDT)
From: William Walster
Subject: Re: New version of GlobSol
To: reliable_computing [at] interval [dot] usl.edu, rbk [at] usl [dot] edu
Replyto: William Walster
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Baker,
You have been busy :)
How about sending the latest f90 source to Russia so they can port it
onto our compiler? I believe you had already sent an earlier version
to them.
I have looked over the paper on handling constants. I will have some
comments when I have a chance to formulate them and write them down.
It might be a good idea if we talk about this paper as well.
Best regards,
Bill
>Date: Wed, 28 Jul 1999 03:53:27 0500
>From: "R. Baker Kearfott"
>Subject: New version of GlobSol
>XSender: rbk5287 [at] pop [dot] usl.edu
>To: reliable_computing [at] interval [dot] usl.edu
>MIMEversion: 1.0
>
>Colleagues,
>
>I have just uploaded a new version of our GlobSol global optimization
>package. Some changes are:
>
>(1) The installation process has been further simplified, and the read.me
> (with instructions) has been clarified.
>
>(2) GlobSol has been restructured so the overall search is now callable as
> a subroutine.
>
>(3) Capability for having "constants" that can be changed during the
> optimization process has been introduced.
>
>(4) Several bugs have been fixed.
>
>(5) The configuration file(s) has been simplified.
>
>See the revised downloading instructions at
>
>http://interval.usl.edu/GlobSol/download_GlobSol.html
>
>for further details.
>
>See the GlobSol home page at
>http://www.mscs.mu.edu/~globsol/
>
>and, in particular, browse the Draft User Guide (available from the GlobSol
>home page) for an explanation of GlobSol.
>
>I have run integration tests with each of the four compiler / OS versions
>I support. (I also provide instructions for modifying the makefile for
>other compiler / OS combinations.) Please contact me with any problems.
>
>
>
>I also wish to point out a new preprint, "On Stopping Criteria in Verified
>Nonlinear Systems or Optimization Algorithms" that is available in
>Postscript or DVI by clicking on the appropriate place in my preprints
>page at
>
>http://interval.usl.edu/preprints.html
>
>Best regards,
>
>Baker
>
>
>R. Baker Kearfott, rbk [at] usl [dot] edu (318) 4825346 (fax)
>(318) 4825270 (work) (318) 9819744 (home)
>URL: http://interval.usl.edu/kearfott.html
>Department of Mathematics, University of Southwestern Louisiana
>USL Box 41010, Lafayette, LA 705041010, USA
>
>
From ownerreliable_computing [at] interval [dot] usl.edu Thu Jul 29 06:39:28 1999
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Date: Wed, 28 Jul 1999 03:53:27 0500
To: reliable_computing [at] interval [dot] usl.edu
From: "R. Baker Kearfott"
Subject: New version of GlobSol
Sender: ownerreliable_computing [at] interval [dot] usl.edu
Precedence: bulk
Original message
Colleagues,
I have just uploaded a new version of our GlobSol global optimization
package. Some changes are:
(1) The installation process has been further simplified, and the read.me
(with instructions) has been clarified.
(2) GlobSol has been restructured so the overall search is now callable as
a subroutine.
(3) Capability for having "constants" that can be changed during the
optimization process has been introduced.
(4) Several bugs have been fixed.
(5) The configuration file(s) has been simplified.
See the revised downloading instructions at
http://interval.usl.edu/GlobSol/download_GlobSol.html
for further details.
See the GlobSol home page at
http://www.mscs.mu.edu/~globsol/
and, in particular, browse the Draft User Guide (available from the GlobSol
home page) for an explanation of GlobSol.
I have run integration tests with each of the four compiler / OS versions
I support. (I also provide instructions for modifying the makefile for
other compiler / OS combinations.) Please contact me with any problems.

I also wish to point out a new preprint, "On Stopping Criteria in Verified
Nonlinear Systems or Optimization Algorithms" that is available in
Postscript or DVI by clicking on the appropriate place in my preprints
page at
http://interval.usl.edu/preprints.html
Best regards,
Baker

R. Baker Kearfott, rbk [at] usl [dot] edu (318) 4825346 (fax)
(318) 4825270 (work) (318) 9819744 (home)
URL: http://interval.usl.edu/kearfott.html
Department of Mathematics, University of Southwestern Louisiana
USL Box 41010, Lafayette, LA 705041010, USA

.
QUIT
From ownerreliable_computing [at] interval [dot] usl.edu Fri Jul 30 07:52:37 1999
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MessageID: <37A1A07D.EB57EE4F [at] math [dot] unikarlsruhe.de>
Date: Fri, 30 Jul 1999 14:54:21 +0200
From: Axel Facius
Organization: Inst. f. Appl. Mathematics, University of Karlsruhe
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To: na.digest@nanet.ornl.gov, optnet@zibberlin.de,
imnetdigest [at] iwr [dot] uniheidelberg.de,
reliable_computing [at] interval [dot] usl.edu,
scicomp [at] fauia10 [dot] informatik.unierlangen.de,
numericinterest [at] validgh [dot] com
Subject: scan 2000: FIRST ANNOUNCEMENT  CALL FOR PAPERS
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scan 2000
9th GAMM  IMACS
International Symposium on
Scientific Computing, Computer Arithmetic,
and Validated Numerics
September 19  22, 2000
Karlsruhe
Germany
http://www.scan2000.de
FIRST ANNOUNCEMENT  CALL FOR PAPERS
This conference continues the series of scansymposia
which have previously been held at Karlsruhe, Basel,
Albena, Oldenburg, Wien, Wuppertal, Lyon, and Budapest
under the joint sponsorship of GAMM and IMACS. These
conferences have traditionally covered the numerical
and algorithmic aspects of scientific computing, with
a strong emphasis on validation and verification of
computed results as well as on arithmetic, programming,
and algorithmic tools for this purpose. The objectives
are to propagate current applications and research as
well as to promote a greater understanding and increased
awareness of the subject matters.
IMPORTANT DATES
March, 31, 2000 Submission of Abstracts
June, 30, 2000 Notification of Acceptance
July, 31, 2000 Return of Registration Form
CONFERENCE CHAIRMEN
o Prof. Ulrich Kulisch
Institute for Applied Mathematics,
University of Karlsruhe
o Prof. Wilfried Juling
Computing Center,
University of Karlsruhe
LOCAL ORGANISATION:
Axel Facius
Institute for Applied Mathematics,
University of Karlsruhe
D76128 Karlsruhe
Germany
For more information and subscription to a mailing list
mail to : info [at] scan2000 [dot] de
or visit: http://www.scan2000.de

> http://www.scan2000.de <

From ownerreliable_computing [at] interval [dot] usl.edu Fri Jul 30 08:03:20 1999
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Date: Fri, 30 Jul 1999 14:57:41 +0200 (MET DST)
From: Zenon Kulpa
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To: reliable_computing [at] interval [dot] usl.edu
Subject: Paper notice
Cc: zkulpa [at] zmit1 [dot] ippt.gov.pl
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I would like to inform you of a semitutorial paper
on application of interval methods in linear mechanics
which finally appeared some time ago. It may be interesting
to you also because its Acknowledgements section contains
the fragment which says:
"[...] greatly appreciated [...] is the help in finding
some literature references and useful discussions on various aspects
of interval methods, kindly provided by members
of the ReliabaleComputing discussion list on the Internet..."
Thank you,
 Zenon Kulpa
_______________________________________________________________

Dr. Zenon Kulpa  Whatever we may want to say,
Institute of Fundamental  we probably won't say
Technological Research  exactly that.
ul. Swietokrzyska 21 
00049 Warszawa, POLAND  Marvin Minsky
______________________________________________________________
tel ++4822/8261281 ext 279 fax ++4822/8269815
URL http://www.ippt.gov.pl/~zkulpa
_______________________________________________________________
Analysis of linear mechanical structures with uncertainties
by means of interval methods

Zenon Kulpa
(Institute of Fundamental Technological Research, Warsaw, Poland)
Andrzej Pownuk
(Silesian Technical University, Gliwice, Poland)
Iwona Skalna
(Academy of Mining and Metallurgy, Cracow, Poland)
Abstract

One of the simplest ways of representation of uncertain
or inexact data, as well as inexact computations with them,
is based on interval arithmetic. In this approach, an uncertain
(real) number is represented by an interval (a connnected
bounded subset) of real numbers which presumably contains
the unknown exact value of the number in question.
Despite its simplicity, it conforms very well to many practical
situations, like tolerance handling or managing rounding errors
in numerical computations. Also, the so called alphacut method
of handling fuzzy sets membership functions is based on
replacing a fuzzy set problem with a set of interval problems.
The purpose of this paper is to investigate possibilities of
and problems with application of interval methods in
(qualitative) analysis of linear mechanical systems with
parameter uncertainties, in particular truss structures
and frames. The paper starts with an introduction to interval
arithmetic and systems of linear interval equations, including
an overview of basic methods for finding interval estimates
for the set of solutions of such systems. The methods
are further illustrated by several examples of practical
problems, solved by our hybrid system of analysis of mechanical
structures. Finally, several general problems with using
interval methods for analysis of such linear systems are
identified, with promising avenues for further research
indicated as a result. The problems discussed include estimation
inaccuracy of the algorithms (especially the fundamental problem
of matrix coefficient dependence), their computational
complexity, as well as inadequate development of methods
for analysis of interval systems with singular matrices.

From ownerreliable_computing [at] interval [dot] usl.edu Fri Jul 30 08:53:35 1999
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From: Bernard Philippe
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reliable computing
Subject: Workshop in France
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ANNOUNCEMENT : Workshop in France :

(Sorry for those who do not read French)
(Most of the talks will be given in French).
Outils pour un calcul numérique fiable
2224 septembre 1999
Paris (Campus Jussieu)
Voir : http://wwwsop.inria.fr/prisme/fiable/workshop.html
Ces journées sont organisées par l'action coopérative FIABLE de l'INRIA.
Thème :
La notion de fiabilité des calculs recouvre deux situations différentes
:
 dans le premier cas, on suppose que les données du problème sont
exactement représentées et on recherche une réponse sûre (c'estàdire
prouvée). C'est le cas
des calculs de géométrie lorsque l'on cherche à placer un point par
rapport à une droite, un cercle, un plan, etc. Ce domaine contient aussi
la recherche de
procédures de localisation de racines de polynômes dans le plan
complexe.
 dans le deuxième cas au contraire, on admet l'existence d'une
incertitude sur les données. Il s'agit alors au minimum d'estimer
l'incertitude sur le résultat et dans le
meilleur des cas de prouver des bornes sur cette incertitude. La
formulation du problème pour avoir un sens doit alors supposer la
continuité du résultat en fonction
des données.
Dans les deux cas, on a recours à des techniques qui reposent sur des
outils communs. En particulier les arithmétiques peuvent être des
aritmétiques entières sur des
nombres de longueur variable et non bornée, des arithmétiques flottantes
de précision classique ou de précision arbitraire, des arithmétiques
d'intervalle, etc. Les
preuves d'encadrement reposent aussi sur les encadrements des fonctions
élémentaires ce qui n'est pas encore établi pour toutes les fonctions
usuelles. Dans le cas
des calculs approchés, il est nécessaire de qualifier le comportement
des algorithmes ; cela peut se faire formellement par une analyse
inverse des erreurs ou a
posteriori sur un jeu de données par une analyse statistique.
Orateurs invités :
T. Granlund (GMP):
J.C. Bergès (CNES):
J. van der Hoeven (CNRS Orsay)
A. Lieutier (Dassault Syst)
F. Randimbivololona (Aérospatiale)
S. M. Rumps (U. Hambourg)
M. Vrahatis (U. Patras)
Organisateurs :
JeanMarie Chesneaux (LIP6, Univ. Pierre et Marie Curie, Paris)
Jocelyne Erhel (Inria, Rennes)
Olivier Devillers (Inria, Sophia A.)
Bernard Mourrain (Inria, Sophia A.)
JeanMichel Muller (ENS, Lyon)
Bernard Philippe (Inria, Rennes)
Paul Zimmermann (Inria, Nancy)
Pour tout contact : Bernard.Philippe [at] irisa [dot] fr
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From ownerreliable_computing [at] interval [dot] usl.edu Fri Jul 30 08:58:46 1999
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Date: Fri, 30 Jul 1999 15:53:36 +0200 (MET DST)
From: Zenon Kulpa
MessageId: <199907301353.PAA13041 [at] zmit1 [dot] ippt.gov.pl>
To: reliable_computing [at] interval [dot] usl.edu
Subject: Re: Paper notice
Cc: zkulpa [at] zmit1 [dot] ippt.gov.pl
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> From: Zenon Kulpa
> To: reliable_computing [at] interval [dot] usl.edu
> Subject: Paper notice
>
> I would like to inform you of a semitutorial paper
> [...]
>
I am awfully sorry  providing abstract of the paper,
I somehow forgot to include the bibliographical reference...
Here goes:
Zenon Kulpa, Andrzej Pownuk, Iwona Skalna:
Analysis of linear mechanical structures with uncertainties
by means of interval methods.
Computer Assisted Mechanics and Engineering Sciences (CAMES),
vol. 5(4), pp. 443477, 1998.
My apologies,
 Zenon Kulpa
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MessageID: <37A1B0B0.5C0F769B [at] eng [dot] umd.edu>
Date: Fri, 30 Jul 1999 10:03:28 0400
From: "Rafi L. Muhanna"
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************************************************************************
Rafi L. Muhanna
Department of Civil Engineering
muhannar [at] eng [dot] umd.edu
University of Maryland (301)
4057965 (VOICE)
College Park, MD 20742, U.S.A. (301)
4052585 (FAX)
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Date: Fri, 30 Jul 1999 09:41:06 0400
From: "Rafi L. Muhanna"
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To: Zenon Kulpa
Subject: Re: Paper notice
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Dear Dr. Kulpa:
You may be interested in the following references:
1. Muhanna, R. L. and Mullen, R. L.(1995). "Development of Interval
Based Methods for Fuzziness in Continuum Mechanics, " Proceedings of
ISUMANAFIPS=9295, pp 145150, September 1720.
2. Koyluglu, U., Cakmak, S., Ahmet, N., and Soren R. K. (1995).
"Interval Algebra to Deal with Pattern Loading and Structural
Uncertainty", Journal of Engineering Mechanics,11491157.
3. Nakagiri, S. and Yoshikawa, N. (1996). "Finite Element Interval
Estimation by Convex Model, " Proc., 7th ASCE EMD/STD Joint Specialty
Conference on Probabilistic Mechanics and Structural Reliability, WP I,
MA, August 79, 278281.
4. Rao, S. S., Berke, L. (1997)." Analysis of Uncertain Structural
Systems Using Interval Analysis, " AIAA Journal, Vol. 35, No. 4.
5. Muhanna, R. L.and Mullen, R. L. (1999). "Formulation of Fuzzy
Finite Element Methods for Mechanics Problems, " ComputerAided Civil
and Infrastructure Engineering (previously Microcomputers in Civil
Engineering), Vol.14, pp 107117.
6. Mullen, R. L. and Muhanna, R. L. (1999). "Bounds of Structural
Response for All Possible Loadings, " Journal of Structural Engineering,
ASCE, Vol. 125, No. 1, pp 98106.
Best regards
Rafi Muhanna
Zenon Kulpa wrote:
> I would like to inform you of a semitutorial paper
> on application of interval methods in linear mechanics
> which finally appeared some time ago. It may be interesting
> to you also because its Acknowledgements section contains
> the fragment which says:
>
> "[...] greatly appreciated [...] is the help in finding
> some literature references and useful discussions on various aspects
> of interval methods, kindly provided by members
> of the ReliabaleComputing discussion list on the Internet..."
>
> Thank you,
>
>  Zenon Kulpa
> _______________________________________________________________
> 
> Dr. Zenon Kulpa  Whatever we may want to say,
> Institute of Fundamental  we probably won't say
> Technological Research  exactly that.
> ul. Swietokrzyska 21 
> 00049 Warszawa, POLAND  Marvin Minsky
> ______________________________________________________________
>
> tel ++4822/8261281 ext 279 fax ++4822/8269815
> URL http://www.ippt.gov.pl/~zkulpa
> _______________________________________________________________
>
> Analysis of linear mechanical structures with uncertainties
> by means of interval methods
> 
> Zenon Kulpa
> (Institute of Fundamental Technological Research, Warsaw, Poland)
> Andrzej Pownuk
> (Silesian Technical University, Gliwice, Poland)
> Iwona Skalna
> (Academy of Mining and Metallurgy, Cracow, Poland)
>
> Abstract
> 
> One of the simplest ways of representation of uncertain
> or inexact data, as well as inexact computations with them,
> is based on interval arithmetic. In this approach, an uncertain
> (real) number is represented by an interval (a connnected
> bounded subset) of real numbers which presumably contains
> the unknown exact value of the number in question.
> Despite its simplicity, it conforms very well to many practical
> situations, like tolerance handling or managing rounding errors
> in numerical computations. Also, the so called alphacut method
> of handling fuzzy sets membership functions is based on
> replacing a fuzzy set problem with a set of interval problems.
> The purpose of this paper is to investigate possibilities of
> and problems with application of interval methods in
> (qualitative) analysis of linear mechanical systems with
> parameter uncertainties, in particular truss structures
> and frames. The paper starts with an introduction to interval
> arithmetic and systems of linear interval equations, including
> an overview of basic methods for finding interval estimates
> for the set of solutions of such systems. The methods
> are further illustrated by several examples of practical
> problems, solved by our hybrid system of analysis of mechanical
> structures. Finally, several general problems with using
> interval methods for analysis of such linear systems are
> identified, with promising avenues for further research
> indicated as a result. The problems discussed include estimation
> inaccuracy of the algorithms (especially the fundamental problem
> of matrix coefficient dependence), their computational
> complexity, as well as inadequate development of methods
> for analysis of interval systems with singular matrices.
> 

************************************************************************
Rafi L. Muhanna
Department of Civil Engineering muhannar [at] eng [dot] umd.edu
University of Maryland (301) 4057965 (VOICE)
College Park, MD 20742, U.S.A. (301) 4052585 (FAX)
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