NA Digest Sunday, September 26, 1993 Volume 93 : Issue 36

Today's Editor:

Cleve Moler
The MathWorks, Inc.

Submissions for NA Digest:

Mail to

Information about NA-NET:

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From: Richard Lehoucq <>
Date: Tue, 21 Sep 93 17:03:55 CDT
Subject: IEEE Trap Handling on SUN Systems

The following is the code needed to be able to trap Floating Point
exceptions within your code on SUN systems in FORTRAN.
Note: for you C programming types, this also works within C software.
Compile the following integer function along with the rest of
your code. You need to compile this and the routines you
want to look at with the -g option if using the debugger.
This has proved instrumental in debugging.

integer function handler(sig,code,sigcontext)
integer sig
integer code
integer sigcontext(5)
print *, ' ieee exception code ',loc(code),
& ' occurred at pc ', sigcontext(4)
call abort

Notes: the name 'handler' is user defined.

The first line of your main program needs the followinf stmt:
ieee= ieee_handler('set','common',handler)
or(or both):
ieee= ieee_handler('set','underflow',handler)

The last line of main program needs the following stmt.
ieee= ieee_handler('clear','all',handler)

notes: 'common' flags overflow, NaN, division by zero.
See man page on ieee_handler for more info.
User defined 'handler' needs to be declared as an
external integer function within the main program unit.
the integer variable 'ieee' is user defined.

Now complie with -g switch, fire up the debugger and make
sure the first command issued within the debugger is:

catch FPE

and type run. Upon encountering an exception, the code pauses execution
and the debugger points to the trapped line and informs user of what exception
occured and at what line number. To continue type cont and you will
encounter the next exception(if any).

An excellent reference is the SUN manual:

Numerical Computation Guide.

DISCLAIMER: I don't profess that this is the best or only way to
trap for floating point exceptions under SUN systems.

-- Richard Lehoucq


From: Jim Van Zandt <>
Date: Wed, 22 Sep 93 08:02:52 -0400
Subject: Help for IEEE Floating Point Woes

Richard Brankin <> writes:
>The following may be of help, for SGI Indigo users anyway,
>and don't forget to link with "-lfpe" when building an executable. This
>has the effect "underflow to zero; bomb out with a traceback when either
>overflow, or divide by zero, or an invalid operand is detected", with
>which I expect most people would be happy.

Can anyone suggest how to get similar effects with Turbo/Borland C?

-- Jim Van Zandt <>


From: Dean Schulze <>
Date: Sat, 25 Sep 1993 16:07:42 -0700 (MST)
Subject: Reality check for an IEEE arithmetic critic

Joe Grcar's complaints about IEEE arithmetic need to be addressed because
some of the things that he says are simply wrong. He made this complaint in
August of 1991:

>There is no machine epsilon.

Yes there is. Numbers can underflow, however, to de-normalized values
that result in a loss of precision. If you think this is a problem how are
you dealing with non-IEEE arithmetic that simply underflows to zero without
telling you about it?

Two weeks ago Grcar published part 2 of his complaint about IEEE
arithmetic which included the following:

>A colleague with a PhD in mechanical engineering just walked
>into may office and said:

>"I like my new SGI Indigo, but I really don't like those NaN
>things it has. I'm rewriting a piece of software and when I
>looked at the output it was all full of NaN's. I found out
>this means I'm dividing by zero somewhere, but where? ..."

Wrong. Under IEEE arithmetic dividing a finite, non-zero number by
zero produces an Inf. Division by zero produces a NaN only if the numerator
is zero, Inf, or NaN. NaNs can also be the result of common programming
errors like reading beyond the bounds of an array.

>By chance I once asked SGI technical support where to find
>documentation on IEEE arithmetic.

Here is an excellent reference that describes IEEE arithmetic:

"What every computer scientists should know about floating-point
arithmetic", David Goldberg, ACM Computing Surveys, v23, #1,
pp. 5-48, 1991.

In response to his posting, I sent Joe Grcar a message that included
this citation. He responded with:

>Pardon me for saying so, but I think your opinion
>of ieee arithmetic would be different if you had
>a real job instead of an academic one. Scientists
>and engineers don't hae time to read arcane
>documentation about trivia in some other field.

Well, I am a scientist and I have to read many papers every month, and
I found that reading Goldberg's paper was beneficial. But if Grcar doesn't
have time to read one paper where does he get the time to write complaints
about IEEE arithmetic for NA Digest? It may be easier to complain than it
is to educate yourself, but then why bother asking for documentation on IEEE
arithmetic in the first place. And why waste the bandwidth on the
network if you are going to be churlish when someone responds with a
reference that you were trying to find?

Also, I think that the people at Motorola, Intel, Sun, the Free Software
Foundation, Symantec, etc., etc., who implement IEEE arithmetic in hardware
and software, will be quite surprised to hear that they don't have real jobs.

I see two problems with IEEE arithmetic, neither one inherent to the
IEEE standard. First, there is a great deal of misinformation floating
around about it (i.e. getting a NaN means that you're dividing by zero).
Probably the worst example I've seen of misinformation about IEEE arithmetic
is P.J. Plauger's book __The Standard C Library__. He makes some ambiguous
comments about IEEE arithmetic in his chapter on the ANSI C math library
that lead you to believe that ANSI C requires IEEE arithmetic. It doesn't,
and he should have explicitly said so instead of making misleading comments.
Goldberg's paper is the cure for this problem.

The second problem is that examples of how to use the features of IEEE
arithmetic in C and Fortran source code are not readily available.
Unfortunately, Goldberg's paper is of no help here. Does anyone have
any examples of profitable use of IEEE arithmetic in their source code
that they can share?

Dean Schulze


From: William E. Schiesser <wes1@Lehigh.EDU>
Date: Fri, 24 Sep 1993 13:46:31 EDT
Subject: Code for Cubic Schroedinger Equation

A complete Fortran code for the method of lines (MOL) integration of the
cubic Schroedinger equation (CSE) is available (on a DOS-formatted diskette).
This code demonstrates the solitons of the CSE, and gives a comparion of the
MOL solution with the analytical solution for the one-soliton case. A paper
pertaining to the CSE, the analytical solution and the MOL approximation is
included with the code. Requests should be sent to:

W. E. Schiesser
Iacocca Hall, D307
Lehigh University
111 Research Drive
Bethlehem, PA 18015 USA

(215) 758-4264 (office)
(215) 758-5057 (fax) (Internet)


From: Bert Buckley <>
Date: Sat, 25 Sep 93 15:46:38 -0700
Subject: Fortran 90 Introduction and Conversion

A preprint of a pair of papers which have been accepted for publication
in TOMS is available via anonymous ftp.

The papers are

1. Conversion to Fortran 90: A Case Study

This describes the conversion of the published TOMS
Algorithm 630 from Fortran 77 to Fortran 90. The paper
can serve as an introduction to many of the features of
Fortran 90. As well, it discusses some of the issues
involved in doing a conversion.

2. A Fortran 90 code for Unconstrained Nonlinear Minimization

This is the converted version of Algorithm 630. It makes
extensive use of many of the new features of Fortran 90.

The code for the Fortran 90 algorithm is also available. Further
details are available in the readme file on the ftp server.

The papers are stored as postscript files. Readers who do not have access
to anonymous ftp or who cannot conveniently handle postscript files may
directly contact the author:

Bert Buckley

The files are available in the directory


on the ftp server

Comments are welcome.


From: E. Smith <>
Date: Thu, 23 Sep 93 13:11 +0100 (BST)
Subject: One day MATLAB Course at RMCS (Cranfield)

One day Course
MATLAB: a tutorial introduction

16 November 1993
Applied Mathematics and Operational Research Group, Royal Military
College of Science.


The course is specifically designed for scientists, engineers and
lecturers who either use routine numerical/matrix calculations in
their specific application area or teach the subject at various
levels. No specialist knowledge of programming or computer science is
required, but participants are expected to have basic knowledge of
computing and to be educated to degree level.


Every participant will receive a comprehensive set of lecture notes
illustrating various features of MATLAB.


The course provides hands-on experience of the MATLAB package, and
will be followed by an in-depth presentation of case studies which
deal with specialist topics from Signal Processing, Control System
Design, Numerical Computations, Splines and Optimization. Most of the
afternoon is devoted to tutorials and the participants will have ample
opportunity to work on a specialist topic of their choice.


The course lectures will be given by the teaching and research staff
of the Applied Mathematics and Operational Research Group under the
direction of Dr. Venkat V.S.S. Sastry.


The fee of #150 (pounds) includes morning coffee, afternoon tea, a
copy of lecture notes and all computer facilities used. (Academic
staff: #112.50 (pounds), research students: #75 (pounds)). Cheques
are payable to RMCS(Cranfield).


To reserve a place on the course please write to Mrs. E. Smith,
Applied Mathematics and Operational Research Group, RMCS, Shrivenham,
Swindon, Wilts., SN6 8LA or Tel: (0793) 785317 or Fax: (0793) 782179
or e-mail:


From: Kerry Anne Landman <>
Date: Fri, 24 Sep 93 09:42:23 EST
Subject: Mathematics-in-Industry Study Group

31 January -- 4 February 1994 at the University of Newcastle

The tenth annual Mathematics-in-Industry Study Group (MISG) will be held at
the University of Newcastle from Monday January 31 to Friday February 4, 1994.

This meeting will be the first under the aegis of the Department of Mathematics
at the University of Melbourne. This department has recently become the new
sponsor of the MISG for a period of three to five years, with Dr Kerry A.
Landman as director.

The MISG brings mathematicians together to work exclusively on real-life
problems facing business and industry. Since 1984 the Study Group has worked
on 63 problems from 39 organisations, with participating companies ranging
from small electronics firms to mining giants. Past problems include
differential equation modelling, operations research, software design,
computational problems, communication theory, statistical problems, and more.
The applications have spanned Australian industry. The major prerequisites
are that the problems should be of practical importance and amenable to
mathematical modelling.

The Study Group is an opportunity for mathematicians to apply their skills
to real problems that present exciting challenges and new research topics,
and for industry to explore the problem solving power of mathematics.

The format of the Study Group will remain as in recent years. On the first
day, a set of scientific problems of industrial origin will be described by
industrial representatives and the assigned problem moderators. The
mathematicians will then work collaboratively with the industry participants
on the problems for three days before presenting their results on the final

Please note the following items

- Financial support will be available on a needs basis for students,
unemployed mathematicians, and academic mathematicians. This will be in
the form of grants for travel costs and a contribution towards
accommodation costs.

- The MISG is keen to ensure greater participation by young mathematicians,
including those at Honours level. Seminars to describe the Study Group and
to encourage participation will be given at a number of universities in
spring this year.

- The MISG is hopeful that the Study Group will stimulate Honours projects
and eventually higher degrees; sponsorship for these projects will be
sought from major companies.

- A student technical essay competition with prize money from a sponsor
is again planned to be held in association with the Study Group.

- If you have any suggestion for suitable Study Group problems, or
industrial contacts who may have a problem for the Study group, please
get in touch with Kerry Landman

To have your name entered on the mailing list for the next circular, contact

Dr Kerry Anne Landman
Department of Mathematics,
University of Melbourne,
Victoria 3052
ph (03) 344 6762, fax (03) 344 4599 or


From: Harriet Cohen <>
Date: Fri, 24 Sep 93 10:57:25 EDT
Subject: Gelfand Celebration

This is a preliminary announcement of the next Statistical Mechanics
Meeting which will take place at Rutgers on December 15th, 16th, and 17th,
1993. A complete program will be sent out in the middle of October. The
tentative list of speakers includes:

M. Avellaneda, N. Berker, W. Bialek, O. Biham,
E. Bodenschatz, H. Brezis, L. Bunimovich, P. Cvitanovic,
R. Goldstein, D. Haldane, P. Hohenberg, A. Karma,
H. Koch, P. Kolodner, A. Majda, S. Orszag,
Y. Pomeau, D. Tsui, D. Vanderbilt

COPIES OF THIS ANNOUNCEMENT THAN YOU WANT. [Even one might be too many.]
Also, if you know of someone who should be on the email-mailing list but
is not, please let me know.

If I do not hear from you, I will assume that everything is okay and will
use the same address for the announcement.

With best wishes,

Professor Joel L. Lebowitz: ARPANET:

P.S. There will be a conference at Rutgers, October 24 - 27, 1993, in
celebration of Israel M. Gelfand's 80th Birthday. Speakers listed are:
K.Aomoto, A.Connes, I.Frenkel, M.Gromov, L.Jeffrey, M.Jimbo, M.Kapranov,
D.Kazhdan, B.Kontsevich, B.Kostant, R.MacPherson, O.Mathieu, C.Moeglin,
A.Polyakov, I.Singer, E.Witten, S.-T. Yau and A.Zamolodchikov

For more information, please contact: Mary Anne Jablonski, Administrative
Assistant Gelfand Conference RUTGERS - Department of Mathematics,
Hill Center, Busch Campus, New Brunswick, NJ 08903, USA Phone:(908)932-3921 FAX:(908)932-5530


From: Omar Hamed <F40M001%SAKSU00.BITNET@VTBIT.CC.VT.EDU>
Date: Wed, 22 Sep 93 12:39:19 +0000 (SLT)
Subject: Postions at King Saud University

We would like to announce the need of our department to hire two
professors in mathematics with high calibre of research and academic
performence specially with the experience of supervision of PH.D. students.
The jobs are going to be available in January, 1994, with very attractive,
tax exempt salaries and allowances for children's education and provision
of free accomodation and health care beside other benefits.

Interseted persons should send their c.v. with recent photo to:

Mathematics Department
College of Science
King Saud University
P.O.Box 2455
Riyadh 11451
Saudi Arabia

For further information you may send e-mail to f40m033@saksu00 (bitnet)
or fax us at ++ 966 1 4676512


From: Gavin Pringle <>
Date: Wed, 22 Sep 93 17:01:38 +0100 (BST)
Subject: Two Post-Doctoral Positions at Napier University, SCOTLAND

(I am posting this as a favour, please do not reply to this email address.
Thanks, Gavin)


12,638 - 14,962 pounds (under review)

The Mathematics Department, as a result of recent funding of SHEFC, is able
to announce the appointment of two-post-doctoral Research Assistants, for a
period of two years initially, to work with the Computational Applied
Mathematics Group, whose interests include Engineering Geometry, Solar
Magnetohydrodynamics, Rational Approximation Theory, Computational Fluid
Dynamics and the Computational N-body problem.

In particular, one Assistant will concentrate on the Computational N-body
problem (including parallel implementation) in the context of Fluid Dynamics.
It is expected that part of the duties of the second Assistant will involve
numerical problems associated with Rational Approximants, although no prior
expertise in this topic is required.

Substantial expertise in Computational Mathematics would be an advantage in
each case. The successful candidates will be expected to have, or to have
submitted for, Ph.D degrees upon taking up their appointments.

Appointment will normally be made within the lowest quartile of the salary

Application forms and further particulars are available from the Head of
Personnel services, Napier University, 219 Colinton Road, EDINBURGH,
EH14 1DJ, SCOTLAND. Tel: +44 31 455 4288 or +44 31 455 4564.
Closing Date: Friday 15 October 1993.


From: Stanley Osher <>
Date: Wed, 22 Sep 93 16:50:58 PDT
Subject: Research and Development Programmer Positions

At rapidly growing numerical image processing company. Bachelor
or Masters degree, excellent C-programming, Unix/systems level,
background in algorithms. Signal/image processing, graphics, numerics,
windows and windows 3.1 development. Excellent computing/scientific
environment. Hardware understanding is desirable.
Please mail resume to: 2800-28th Street, Suite 101, Santa Monica, CA
Stan Osher


From: Luis Mandel <>
Date: Fri, 24 Sep 1993 10:41:45 +0200 (MET DST)
Subject: Faculty Positions at SUNY-Buffalo

Faculty Positions

The Department of Computer Science seeks candidates for faculty
positions at the Assistant or Associate Professor level. We will
consider only those candidates who demonstrate exceedingly high
research promise. We are seeking candidates in applied and ex-
perimental areas of computer science as well as candidates who
will collaborate with researchers in other disciplines. We are
especially keen on attracting faculty in parallel computing and
systems in order to continue to build our current base in those

The department currently has 15 tenure-track faculty, 3 full-time
lecturers, and 9 research and adjunct faculty members. Primary
research areas include: artificial intelligence, complexity
theory, computer vision, numerical linear algebra, parallel algo-
rithms, pattern recognition, programming languages, systems and
VLSI. Department members are actively engaged in interdisci-
plinary research with the Graduate Group in High Performance Com-
puting, Cognitive Science Center, Medical Foundation of Buffalo,
NSF National Center for Geographic Information and Analysis, and
the USPS Center of Excellence for Document Analysis and Recogni-

Address applications, including a cover letter, curriculum vitae,
a one-page research statement, and names and addresses of three
references to: Professor Anthony Ralston; Chair, Recruiting Com-
mittee; 226 Bell Hall; Department of Computer Science; State
University of New York; Buffalo, NY 14260-2000. E-mail: Phone: (716) 645-3180. FAX: (716) 645-

SUNY is an Equal Opportunity/Affirmative Action employer.


From: Richard Brualdi <>
Date: Thu, 23 Sep 1993 08:28:07 -0500 (CDT)
Subject: Contents, Linear Algebra and its Applciations

Volume 193

Eduardo Marques de Sa (Coimbra, Portugal) and Maria-Jose Sodupe (Bilbao, Espana)
Characterizations of *Orthant-Monotonic Norms 1

Gerhard Schmeisser (Erlangen, Germany)
A Real Symmetric Tridiagonal Matrix With a Given Characteristic
Polynomial 11

Dietrich von Rosen (Uppsala, Sweden)
Homogeneous Matrix Equations and Multivariate Linear Models 19

John A. Kaliski and Yinyu Ye (Iowa City, Iowa)
An Extension of the Potential Reduction Algorithm for Linear
Complementarity Problems With Some Priority Goals 35

Zinovy Reichstein (Berkeley, California)
On Automorphisms of Matrix Invariants Induced From the Trace Ring 51

Karla Rost (Chemnitz, Germany)
Generalized Lyapunov Equations, Matrices With Displacement
Structure, and Generalized Bezoutians 75

M. C. Gouveia (Coimbra, Portugal)
Generalized Invertibility of Hankel and Toeplitz Matrices 95

L. J. Landau and R. F. Streater (London, England)
On Birkhoff's Theorem for Doubly Stochastic Completely Positive
Maps of Matrix Algebras 107

Karlheinz Grochenig (Storrs, Connecticut)
A Discrete Theory of Irregular Sampling 129

Karla Rost (Chemnitz, Germany)
Generalized Companion Matrices and Matrix Representations for
Generalized Bezoutians 151

Vlad Ionescu and Martin Weiss (Bucharest, Romania)
Continuous and Discrete-Time Riccati Theory: A Popov-Function
Approach 173

R. Kit Kittappa (Millersville, Pennsylvania)
A Representation of the Solution of the nth Order Linear
Difference Equation With Variable Coefficients 211

Author Index 223

Special Issues in Progress

1. Proceedings of the Second Conference of the International Linear Algebra
Society at Lisbon; special editors are J. A. Dias da Silva, Chi-Kwong Li, and
Graciano de Oliveira. To appear as Volume 197, January 15, 1994.

2. Special Issue Honoring Ingram Olkin: special editors are Friedrich
Pukelsheim, George P. H. Styan, Henry Wolkowicz, and Ion Zaballa. To appear as
Volume 199, March 1, 1994.

3. Special Issue Honoring Marvin Marcus; special editors are Bryan E. Cain,
Moshe Goldberg, Robert Grone, and Nicholas J. Higham. Submission deadline:
December 31, 1992. Details in Volume 161, January 15, 1992.

4. Linear Systems and Control, Third Special Issue; special editors are A. C.
Antoulas, P. A. Fuhrmann, M. L. J. Hautus, and Y. Yamamoto. Submission
deadline: November 30, 1992. Details in Volumes 162-164, February 1992.

5. Special Issue Honoring Chandler Davis; special editors are Rajendra Bhatia,
Shmuel Friedland, and Peter Rosenthal. Submission deadline: March 31, 1993.
Details in Volume 169, May 1992.

6. Proceedings of the Third Conference of the International Linear Algebra
Society at Pensacola; special editors are Dianne P. O'Leary, Leiba Rodman, and
Helene Shapiro. Submission deadline: June 30, 1993. Details provided with the
conference announcement.

7. Proceedings of the conference ``Matrices and Graphs'' in honor of John
Maybee's 65th birthday, held at Boulder, Colorado, May 7, 8, 1993. Special
editors: C. R. Johnson and J. R. Lundgren. Submission deadline: August 31,
1993. Details provided with the conference announcement.

8. Fourth Special Issue on Linear Algebra and Statistics; special editors are
Jeffrey J. Hunter, Simo Puntanen, and George P. H. Styan. Submission deadline:
June 30, 1993. Details in Volume 177, December 1992.

9. Proceedings of the workshop ``Nonnegative Matrices, Applications and
Generalizations'' and the Eighth Haifa Matrix Theory conference held at Haifa,
Israel, May 31-June 4 and June 7-June 10, 1993, respectively. Special editors:
S. Friedland, D. Hershkowitz, and R. Loewy. Submission deadline: September 15,
1993. Details provided with the conference announcement.

10. Special Issue Honoring Miroslav Fiedler and Vlastimil Ptak; special
editors are Wayne Barrett, Angelika Bunse-Gerstner, and Nicholas Young.
Submission deadline: August 31, 1993. Details in Volume 179.

11. Proceedings of the Fourth Conference of the International Linear Algebra
Society at Rotterdam; special editors are Harm Bart, Ludwig Elsner, and Andre
Ran. Submission deadline November 30, 1994. Details provided with the
conference announcement.

12. Special issue honoring J. J. Seidel; special editors are Aart Blokhuis,
Willem H. Haemers and Alan J. Hoffman. Submission deadline: August 30, 1994.
Details in Volume 193, November 1, 1993.

Special issues are available to individuals at a reduced rate. For further
information, please contact Yusuf Guvenc, Journals Customer Service, Elsevier
Science Publishing Co., 655 Avenue of the Americas, New York, NY 10010; Tel.
212-633-3955; Fax 212-633-3990.


From: SIAM <>
Date: Fri, 24 Sep 93 12:03:06 EST
Subject: Contents, SIAM Mathematical Analysis

Table of Contents
SIAM J. Math. Anal.
January 1994, Vol. 25, No. 1

On Nonstationary Motion of a Compressible Barotropic Viscous Capillary Fluid
Bounded by a Free Surface
W.M. Zajaczkowski

Solutions for Two Dimensional System for Materials of Korteweg Type
Harumi Hattori and Dening Li

Instability of Planar Interfaces in Reaction Diffusion Systems
Masaharu Taniguchi and Yasumasa Nishiura

Tikhonov Regularization for Finitely and Infinitely Smoothing Operators
B.A. Mair

Regularizing Microscopes and Rivers
Marc Diener

A New Standard Isometry of Developable Surfaces in CAD/CAM
Erwin Kreyszig

Existence of a Homoclinic Orbit of the Lorenz System by Precise Shooting
Brian Hassard and Jianhe Zhang

The Addition Formula for Continuous q-Legendre Polynomials and Associated
Spherical Elements on the SU(2) Quantum Group Related to Askey-Wilson Polynomial
H.T. Koelink

Basic Hypergeometric Functions and the Borel-Weil Construction for UQ(3)
M.A. Lohe and L.C. Biedenharn


From: Iain Duff <>
Date: Sat, 25 Sep 93 08:19:52 +0100 (BST)
Subject: Contents, IMA Numerical Analysis

IMA Journal Numerical Analysis.
Volume 13, Number 4. October 1993.

Pruess S 2
Shape preserving C cubic spline interpolation.

Chandler-Wilde S N
Some uniform and stability and convergence results for integral
equations on the real line and projection methods for their solution.

Achdou Y and Pironneau O
The chi-method for the Navier-Stokes equation.

Binding P A, Browne P J, and Ji X
A numerical method using the Prufer transformation for the calculation
of eigenpairs of two parameter Sturm-Liouville problems.

Fuchs P M
A global negative result on algebraic stability and a special positive
result on linear stability of generalized IRK methods.

Sloan I H, Dat Tran, and Fairweather G
A fourth-order cubic spline method for linear second-order two-point
boundary value problems.


End of NA Digest