NA Digest Sunday, July 4, 1999 Volume 99 : Issue 27

Today's Editor:
Cleve Moler
The MathWorks, Inc.

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From: Jack Dongarra <>
Date: Fri, 02 Jul 1999 12:46:33 +0200
Subject: LAPACK, Version 3.0 is Available

LAPACK, Version 3.0 is available

LAPACK is a library of numerical linear algebra subroutines designed for
high performance on workstations, vector computers, and shared memory
multiprocessors. (See for details.)

Release 3.0 of LAPACK introduces new routines, as well as extending the
functionality of existing routines. The most significant new routines
and functions are:
1) singular value decomposition (SVD) computed
by the divide-and-conquer method, (xGESDD)
2) SVD based divide-and-conquer least squares solver (xGELSD)
3) new simple and expert drivers for the generalized nonsymmetric
eigenproblem (xGGES,xGGEV,xGGESX,xGGEVX)
4) new generalized symmetric eigenproblem drivers (xHBGVD/xSBGVD,
5) symmetric eigenproblem drivers using fast but relative robust
eigenvector computations (xSTEGR, xSYEVR/xHEEVR, SSTEVR)
6) a faster QR decomposition with column pivoting (xGEQP3)
7) a faster solver for the rank-deficient least squares problem (xGELSY)
8) a blocked version of xTZRQF (xTZRZF), and associated xORMRZ/xUNMRZ
9) solver for the generalized Sylvester equation (xTGSYL)
10) computational routines (xTGEXC, xTGSEN, xTGSNA)

One of the primary design features of the LAPACK library is that all
releases are backward compatible. This release of LAPACK introduces
routines that exploit IEEE arithmetic. We have a prototype of a new
algorithm (xSTEGR), which may be the ultimate solution for the symmetric
eigenproblem on both parallel and serial machines. This algorithm has
been incorporated into the symmetric eigenproblems for version 3.0 of
LAPACK, and will soon be propogated into the SVD, and the SVD-based
least squares solver. We expect to also propagate this algorithm into

Bug fixes, code modifications, and/or commenting changes have also
occurred. For complete information, please refer to the release_notes
file in the lapack directory on netlib.

There are LAPACK bindings available for Fortran 90, C, and Java.

The third edition of the LAPACK Users' Guide is in preparation and will
be available soon via the URL:



From: Deborah Poulson <>
Date: Tue, 29 Jun 99 11:06:47 -0500
Subject: Looking for Copy of Ekeland/Temam Book

by Ivar Ekeland and Roger Temam in our Classics series. I have one
copy of the book, but I'd like to get another. Do you have a copy
you can part with? I'll be happy to replace it with the SIAM
Classics edition when it publishes.


Deborah Poulson
Developmental Editor


From: Rolf Stenberg <>
Date: Thu, 1 Jul 1999 11:55:08 +0200
Subject: New Address for Rolf Stenberg

I have taken a new position as professor of mathematics at Tampere
University of Technology. My starting date there will be August 1,
1999, and my new addresses will be the following. (My e-mail will
work from the end of August onwards.)

Rolf Stenberg
Tampere University of Technology
Department of Mathematics
PL 527
FIN-33101 Tampere

Phone: +358 3 365 2436
Telefax:+358 3 365 3549


From: Kelly Black <>
Date: Mon, 28 Jun 1999 07:03:57 -0400 (EDT)
Subject: New Undergraduate Math Journal

Please tell your students about our new electronic Mathematics Journal
for Undergraduates. Rose-Hulman Institute of Technology is pleased to
announce that the first issue of the Rose-Hulman Undergraduate
Mathematics Journal will be published in March 2000. The journal is
devoted entirely to papers written by undergraduates on topics related
to mathematics.

Call for Papers

The journal welcomes articles containing new results, new and
interesting proofs of old results, historical developments of a theorem
or area of mathematics, relationships between areas of mathematics
and/or other fields of study, or interesting applications of
mathematics. The paper should be accessible and interesting to a wide
range of readers. In addition to having a reviewing process, we ask that
a mathematician who knows the student's work write a letter supporting
the paper. Please see our web site for more details, and if you
should have any questions, please send an email to

Sincerely yours,
Roger Lautzenheiser, Editor
Rose-Hulman Undergraduate Mathematics Journal
Terre Haute, IN 47803


From: Dirk Laurie <>
Date: Tue, 29 Jun 1999 18:51:14 +0200 (SAST)
Subject: Condition Number of an All-zero Matrix

We define the condition number of a matrix as
(*) cond(A) == norm(A)*norm(inv(A))
This works nicely even when A is singular. Using modern IEEE arithmetic,
you get a pleasing infinity for a matrix like [0 0;0 1]. But when A is
all zeros, the definition gives zero times infinity, which translates
to not-a-number.

I can't think of any application where one would need cond(A) to exhibit
this behaviour. Rather, since cond(A) is an indicator of singularity,
it should also be infinite when A is all zeros. Should we not rather use
(*) only when A is nonsingular, and define cond(A) to be infinite when
A is singular?

Perhaps I should explain what set me onto this. I was modifying code
for a tridiagonal solver that uses 2x2 pivots whenever the 1x1 pivot is
too close to zero, to give me a block-tridiagonal solver. Now the block
analogue of a zero pivot, I thought, is a singular matrix, so I put in
a test that selects a 2x2 block pivot whenever the 1x1 block pivot is
singular, which in standard numerical practice is
"if cond(D)>1/eps, %select 2x2 pivot."
My routine promptly failed to select a 2x2 pivot on my very first test
case, which was the block 2x2 system:
[[0 0;0 0] [1 0;0 1]; [1 0;0 1] [0 0;0 0]]

The routine works now, because the test has been changed to
"if cond(D)<1/eps, %select 1x1 pivot".
All conditionals involving a NaN (even "NaN==NaN") test false!
But it feels like a swindle.

Dirk Laurie


From: David Steinman <>
Date: Thu, 1 Jul 1999 19:03:56 -0400
Subject: Unique ID for Triplet of Integers

I am looking for a computationally simple formula that, given a triplet of
natural numbers (a,b,c) produces a unique integer ID. This ID should be the
same regardless of the order of the triplet (i.e. 1,5,4 and 4,1,5 should
give the same ID number), and also a!=b!=c.

I guessed at a promising formula, ID = ab+bc+ca, but a brute force loop (I'm
not a mathematician so I couldn't prove this elegantly) showed that it does
not produce a unique ID. I imagine a problem like this has been tackled in
number theory or cryptography, but I figured maybe someone here would have a

Any help would be greatly appreciated.

David A. Steinman, Ph.D.
Scientist, J.P. Robarts Research Institute
Assistant Professor, U. Western Ontario

Imaging Research Labs
J.P. Robarts Research Institute
100 Perth Drive, P.O. Box 5015
London, Ontario, Canada N6A 5K8
(519) 685-8300 x34113 (Office)
(519) 663-3900 (Fax)


From: Adhemar Bultheel <>
Date: Fri, 2 Jul 1999 15:12:41 +0200 (MET DST)
Subject: New Book, Orthogonal Rational Functions

It is a pleasure to announce our new book

Orthogonal Rational Functions

A. Bultheel, Katholieke Universiteit Leuven,
P. Gonzalez-Vera, Universidad La Laguna,
E. Hendriksen, Universiteit van Amsterdam
O. Njastad, Norges Teknisk-Naturvitenskapelige Universitet

Cambridge Monographs on Applied and Computational Mathematics series, vol 5.
Cambridge University Press, 1999

Binding: Hardback
Bibliographic information:
228 x 152 mm 407pp 18 line diagrams
ISBN: 0 521 65006 2
15 April 1999
Price: =A3 37.50


This book generalises the classical theory of orthogonal
polynomials on the complex unit circle, or on the real
line to orthogonal rational functions whose poles are
among a prescribed set of complex numbers. The first
part treats the case where these poles are all outside
the unit disk or in the lower half plane.
Classical topics such as recurrence relations, numerical quadrature,
interpolation properties, Favard theorems,
convergence, asymptotics, and moment problems are
generalised and treated in detail. The same topics are
discussed for the different situation where the poles are
located on the unit circle or on the extended real line. In
the last chapter, several applications are mentioned
including linear prediction, Pisarenko modeling, lossless
inverse scattering, and network synthesis. This theory
has many applications in theoretical real and complex
analysis, approximation theory, numerical analysis,
system theory, and in electrical engineering.

Chapter Contents

List of symbols;
1. Preliminaries;
2. The fundamental spaces;
3. The kernal functions;
4. Recurrence for orthogonal functions;
5. Quadrature;
6. Interpolation;
7. Density of the rational functions;
8. Favard theorems;
9. Convergence;
10. Moment problems;
11. The boundary case;
12. Some applications;


From: Tsorng-Whay Pan <>
Date: Tue, 29 Jun 1999 17:55:59 -0500 (CDT)
Subject: Conference in Honor of Jacques-Louis Lions

Differential Equations and their Applications

in honor of
Jacques-Louis Lions'
70th Birthday

U. of Houston, Hilton Conference Center
Houston, Texas
October 7-9, 1999


Avner Friedman Martin Golubitsky
Michael Gorman Matthias Heinkenschloss
S. Lennart Johnsson Daniel D.Joseph
Hideo Kawarada Herbert B. Keller
Petr Kloucek Donald Kouri
Didier Lapeyre Ralph Metcalfe
J. Tinsley Oden Danny Sorensen
Bruno Stoufflet Authur Vailas
Mary F. Wheeler

The conference will feature lectures that address recent advances
and current research in the following areas:

(1) Partial differential equations modeling for phenomena from natural
sciences and engineering, including applications from physics,
chemistry, bio-engineering, aerospace engineering, and material

(2) Mathematical methods for the solution of partial differential

(3) Computational methods for partial differential equations.

All who are interested are welcome to attend. For additional information
about this conference, please contact

Drs. G.E. Etgen and R. Glowinski
Department of Mathematics
University of of Houston
Houston, TX 77204-3476

or visit our conference web page

This conference is sponsored by the University of Houston and
the IMA at the University of Minnesota.


From: Sun Wenyu <>
Date: Wed, 30 Jun 1999 21:06:23 -0300 (EST)
Subject: Conference in Nanjing on Optimization and Numerical Algebra


Nanjing Normal University, Nanjing, China
September 27--30, 1999

Second Announcement and Call for Paper

Nanjing is a historical and modernized city known as "Ancient Capitals of
Six Dynasties" which is full of tourism attractions. The Nanjing International
Conference aims to review and discuss recent advances and promising research
trends in some areas of Optimization and Numerical Algebra.

The TOPICS INCLUDE Linear and Nonlinear Programming, Convex and Nonconvex
Programming, Nonsmooth Optimization, Global Optimization, Stochastic
Programming, Multiobjective Optimization, Network Programming, Variational
Inequalities, Linear and Nonlinear Systems of Equations, Least-Squares
Problems, Computation of Eigenvalue Problems, Matrix Computation and
Generalized Inverses, Applications of Optimization and Numerical Algebra.

The Organizing Committee is headed by L.Qi (Sydney, Australia) and Y.Yuan
O.Axelsson (The Netherlands), D.Cai (Beijing), T.F.Coleman(USA), S.C.Fang(USA),
G.C.Feng (Changchun), M.C.Ferris (USA), M.Fukushima(Japan), W.Gander
(Switzerland), J.Y.Han (Beijing),E.X.Jiang (Shanghai),Bo Kagstrom (Sweden),
P.Kall(Switzerland),W.W.Lin (Taiwan), Z.Nashed (USA),W.Niethammer(Germany),
L.Qi (Australia),D.Ralph (Australia),E.W.Sachs (Germany),Z.Shen(Nanjing),
J.Stoer(Germany), J.Sun(Singapore),J.G.Sun (Sweden), K.Tanabe(Japan),
K.L.Teo(Hong Kong),A.J.Wathen (UK), W.Yu(Shanghai), Y.Yuan (Beijing),
J.Zhang(Hong Kong), X.Zhang (Beijing), Y.Zhang(USA).

All speakers, including invited speakers, should submit an abstract of
LaTex file, not exceed one page, via e-mail to
before July 30, 1999. The hard copy of the abstract will also be accepted,
and should be sent before the same time deadline to Ms. Wang Wei,
secretary of conference office, 99'ONA. Notification of acceptance of
contributed talks will be sent by August 20, 1999.
The full registration fee is 300US$ which covers registration, three meals
per day during the conference, coffee break, abstract collection, one
reception, one banquet, half-day city tour. The full registration fee for
student is 150US$. A special volume of the Annals of Operations Research (AOR)
is planned for this conference. In addition, a post-conference self-paid
tour to Yellow Mountain (three-day tour) will be arranged from October 1
(Friday) through to October 3 (Sunday). We also call for 1999 Nanjing
Award in Optimization and numerical Algebra for Excellent papers of young

For further information please contact
Ms. Wang Wei, Secretary of Conference Office, 99'ONA
School of Mathematics and Computer Science, Nanjing Normal University
Nanjing 210097, China.
Email:, Tel/Fax: +86-25-372-0604
or check WWW websites of,, html/meeting.html.


From: Paul Armand <>
Date: Tue, 29 Jun 1999 11:43:59 +0200 (MET DST)
Subject: Postdoctoral Position at Elf, France

Un emploi postdoctoral est a pourvoir au Centre de Recherche de
Elf Solaize, Lyon (FRANCE).

Le candidat integrera un projet de recherche sur l'optimisation d'une
unite de raffinage de produits petroliers. Des connaissances en
optimisation numerique et en programmation (fortran et matlab sur PC)
sont requises.

La preference sera, en principe, donnee a un candidat etranger.

Le contrat peut debuter immediatement, pour une duree d'un an. Le
salaire est d'environ 11000FF mensuel. Le lieu de travail est
a Solaize (10 km au sud de Lyon).

Les candidatures, sous forme d'un curriculum vitae, sont a envoyer a:
(voie postale ou email):

Paul Armand
LACO - Departement de Mathematiques tel: (33) 05 55 45 73 30
Faculte des Sciences fax: (33) 05 55 45 73 22
123, avenue Albert Thomas email:
87060 Limoges Cedex FRANCE


From: Andrew Peplow <>
Date: Tue, 29 Jun 1999 16:13:32 +0200
Subject: Postdoctoral Position at The University of the West of England

Applications are invited for a EPSRC Postdoctoral Fellow (Ref R/224)
at the Faculty of Computer Studies & Mathematics, University of the
West of England, Bristol.

This post will develop innovative boundary element algorithms for elastic
wave scattering from objects in layered media and is fixed term for a
period of 15 months, in the first instance. The successful candidate will
work closely with the Royal Technical University in Stockholm (KTH) and be
expected to participate in occasional overseas trips. Applicants should have
experience in large scale scientific computing for boundary element methods.
Experience in wave propagation and/or modern iterative techniques will also
be an advantage. Please contact Dr A Peplow on e mail

The full advertisement and further particulars are available from:

Salary will be in the range =A319,000 - =A324,000.
Closing date: Friday 9th July 1999.


From: Prabir Daripa <>
Date: Fri, 2 Jul 1999 04:41:11 -0500 (CDT)
Subject: Postdoctoral Position at Texas A&M

(NOTE the email address carefully)
Send your responses to:

Applications are invited for one postdoctoral position with
Dr. Prabir Daripa in the Institute of Scientific Computation
at Texas A&M University.

The project is in the area of scientific computation and requires
knowldge of solving partial differential equations using numerical
methods. Implementation of fast algorithms on serial as well as parallel
machines will be required. The applicant for this project must have
expertise in computations and developing codes on serial and parallel
machines. Strong proficiency in programming using C in a Unix environment
is a must.

The position is open immediately and is initially for 10-12 month period
with full time research. Appointment may be extended further depending
upon performance and the funding situation. A recent Ph.D. in computer
science/numerical mathematics/computational science is required.
Post-Ph.D experience in a research environment is a plus.

Applications should be in the form of a full curriculum vitae
together with the names of three referees and copies of relevant
publications. They should be sent either by e-mail at the address

or by airmail to:

Prabir Daripa
Department of Mathematics
Texas A&M University
College Station
Texas 77843-3368

Phone (409) 845-1204
Fax (409) 862-4190

Texas A&M University is an Equal Opportunity Employer.


From: Tim Phillips <>
Date: Fri, 02 Jul 1999 10:20:57 +0100
Subject: Studentship at University of Wales, Aberystwyth


The Applied Mathematics Research Group at Aberystwyth has an EPSRC Quota
PhD Studentship available. Join a lively, friendly, interdisciplinary
research group with a Grade 5 research rating, working in very attractive
rural surroundings. Benefit from our many links with industry in the UK
and overseas, and from our active collaboration with many research groups
in Europe, the USA, and Australia. All our recent PhD graduates have
found good jobs in industry or academia.

Candidates should have a background in at least one of the following topics:
applied analysis; perurbation methods; partial differential equations;
numerical analysis or computational mathematics; continuum mechanics;
experimental fluid dynamics; or any branch of engineering with a nontrivial
mathematical component.

In addition a bursary for travel to centres of collaboration in Europe
will be awarded to the successful candidate.

Contact: Dr Tim Phillips
(Tel 01970 622769; e-mail


From: Jacek Gondzio <>
Date: Fri, 02 Jul 1999 18:20:09 +0100
Subject: Research Assistant Position at University of Edinburgh

Department Mathematics and Statistics
University of Edinburgh

Research Assistant in Optimisation

You will work on the parallel implementation
of large-scale optimization techniques.

You should have a background in mathematics, physics
or computer science with a strong interest in computing.

The post is for 15 months in the first instance
from 1 October 1999.

Salary on the AR1B scale 15,735 to 17,570pa.
An exceptional candidate may be appointed for a shorter period
on the AR1A scale 15,735 to 23,651pa.

The project will be carried out under the supervision
of Dr Jacek Gondzio to whom informal enquiries may be made
(tel: +44 131 650 8574, fax +44 131 650 6553,

Further particulars, including details of the application procedure,
should be obtained from the Personnel Office, 1 Roxburgh Street,
Edinburgh EH8 9TB. Please quote reference 776546
Closing date for receipt of applications is 31 July 1999.


End of NA Digest