NA Digest Sunday, April 14, 1991 Volume 91 : Issue 15

Today's Editor: Cleve Moler

Today's Topics:


From: Cleve Moler <>
Date: Sun Apr 14 19:55:54 EDT 1991
Subject: NA Net List Tops 2000 Names

This week's issue of the NA Net News Digest is being sent
to an electronic mailing list containing 2026 entries.


From: George Corliss <>
Date: Mon, 8 Apr 91 7:43:59 CDT
Subject: Splines in Sailmaking

In last week's NA Digest, Gordon F. Royle
<> asked about applications of
numerical analysis. Readers might be interested in applications of
splines to sailmaking.

Some time ago, I did some consulting for a firm which makes
sails for racing and cruising yachts. At that time (and still
today), workers spread out the sail cloth on a large, soft gym
floor. They use ice picks to constrain long (I saw a 60 footer in
use) fiberglass battens to interpolate as many as 20-30 points with
the desired curve.
My work involved computerizing a portion of the design process
to drive large (6' x 100') flat bed plotters. In some settings, we
used cubic splines to interpolate many points. In other settings,
we wanted to interpolate 3 - 5 points with slopes specified at each
point. We discovered that when the sail was set on the yacht, many
expericenced racing sailors could distinguish between a piecewise
quadratic and a piecewise cubic spline. The sailor could not say
what was different, but the cubic splines produced noticably
"better looking" (and faster) sails.
We also used cubic splines to control the acceleration and
deceleration of the head on the flat bed plotter. The head weighed
20 pounds. It was driven by servo motors using bicycle chains.
The piecewise linear acceleration functions supplied by the plotter
manufacturer burned out several motors before we replaced them with
cubic spline acceleration functions.
My client installed 25 of these plotters in sail lofts around
the world. They contributed to advances in sails for America's Cup
yachts, for example. Before the advent of this plotter technology,
the panels in nearly all sails were horizontal. If you look in a
magazine devoted to yacht racing today, you will see pictures of a
bewildering variety of panel layouts designed for the stress loading
in the sails. By the way, much of the fundamental work to determine the
stress in working sails was hydrodynamics work done by a Danish
physicist for the same firm.
We never published any of this work because of the firm's
desire to maintain a competative advantage, but I do not think this
discussion compromises any trade secrets. By now, it is old news.

George F. Corliss


From: Gene H. Golub <>
Date: Fri, 12 Apr 91 15:23:20 EMT
Subject: New Book by Golub and Ortega

Jim Ortega and I have recently revised and updated the 1981 book
"Introduction to Numerical Methods for Differential Equations" by
Ortega and Bill Poole. The revision is being published by Academic
Press under the new title "Scientific Computing and Differential
Equations: An Introduction to Numerical Methods." Academic is
shooting to have the book out by August so it would be available for
fall semester classes. We hope you find this book of interest; we'd
be pleased to hear your constructive comments.
For further information on ordering the book, contact Dave Pallai
at Academic Press, (617)876-3901, cdp!

Gene Golub


Date: Fri, 12 Apr 91 14:57 EDT
Subject: New Book from SIAM

Title: Mathematical and Numerical Aspects of Wave Propagation Phenomena
Editors: Gary Cohen, Laurence Halpern, Patrick Joly
Series: Proceedings -- #50
No. of Pages: 808, softcover
List Price: $68.00

Description: The first international conference on mathematical and numerical
aspects of wave propagation phenomena was held in Strasbourg, France, from
April 23 to 26, 1991. The conference program covers a broad range of topics,
both from mathematical and physical points of view. The main domain
interest was numerical methods, such as finite difference method (FDM),
finite element method (FEM), spectral methods, etc., for solving wave

For additional information please contact SIAM, 3600 University City
Science Center, Philadelphia, PA 19104-2688; telephone: 215-382-9800;
fax: 215- 386-7999; e-mail:


From: Alan Edelman <>
Date: Sat, 13 Apr 91 13:48:05 PDT
Subject: The First Annual Large Dense Linear System Survey

This is a second call for responses to the first annual large dense
linear algebra survey from issue 12 of this digest. Those of you
who are solving large dense linear systems of equations for whatever
purpose are invited to stand up and be counted. If you know others
who would not be reading this digest, could you invite them to fill out
the survey?

The form can be readily found in issue 12 of this digest or by anonymous
FTP from in /pub/edelman/survey1991, or by request
to me. Thank you.

-- Alan Edelman
Dept of Mathematics
University of California
Berkeley, CA 94720


From: Olof Widlund <widlund@WIDLUND.CS.NYU.EDU>
Date: Sat, 13 Apr 91 16:11:44 -0400
Subject: Douglas Arnold Wins Giovanni Sacchi Landriani Prize

Douglas Arnold wins the First Giovanni Sacchi Landriani Prize

On February 28, the first Giovanni Sacchi Landriani Prize was awarded to
Professor Douglas N. Arnold of the Pennsylvania State University Mathematics
Department. The selection was made by a committee of the Istituto Lombardo,
Accademia di Scienza e Lettere, of Milan Italy.

The Prize honors Dr. Giovanni Sacchi Landriani, a very promising young
Italian numerical analyst, who died tragically in a traffic accident.

Dr. Arnold received the award of 10000000 Italian Lire in recognition of
his work on elasticity, collocation and boundary element methods, mixed
finite element methods and other problems of numerical analysis.


From: Andy Pollard <>
Date: Mon, 8 Apr 91 08:09:49 MDT
Subject: Finite Element Methods for 3D Diffusion Equation

Problem description

I have a finite difference program which solves a three-dimensional
modified heat equation of the form,

Du = cdu/dt + g(u,t)

where D is a Laplacian and g(u,t) is a nonlinear source term dependent
on u and t. The computational expense in the problem is associated with
the the calculation of g, which involves numerous complex exponentials
on each iteration in the solution. As one possible way to reduce my grid
size without introducing discretization error, I am interested in
implementing a finite element code to evaluate the Laplacian. Are there
general FEM routines which might be tailored to my application?

Thanks in advance

Andy Pollard (
CVRTI - Building 500
The University of Utah
Salt Lake City, UT 84112


From: Kathryn Brenan <>
Date: Mon, 08 Apr 91 09:09:50 -0700
Subject: Shampine/Gordon Integrator in C

Does anyone know if the Shampine/Gordon integration
software (Adams numerical integration code for ordinary
differential equations) has been rewritten in C? I am
looking a public domain version, before similar work
is undertaken here.

Thanks in advance.

Kathryn Brenan

The Aerospace Corporation
P.O. Box 92957
Los Angeles, CA 90009-2957


From: Tony Lin <>
Date: Wed, 10 Apr 91 17:09:02 PDT
Subject: Software for Hypergeometric Function Sought

Does anyone know where I can obtain a fortran subroutine for
calculating the hypergeometric function 2F1(a,b,c;z)? (Not
the confluent case)

Tony Lin


From: Russell Ruby <>
Date: 11 Apr 91 02:25:25 GMT
Subject: Software for Prolate Spheroidal Wave Functions Sought

Does anyone know of any package (public domain or otherwise)
which can evaluate prolate spheroidal wave functions?

Russell Ruby
phone (503)-737-5167


From: Daniel P. Giesy <>
Date: Thu, 11 Apr 91 14:13:51 EDT
Subject: Some Remarks on Reciprocal Pythagorean Sums

George Miel, writing in:

NA Digest Sunday, March 24, 1991 Volume 91 : Issue 12

NA Digest Sunday, March 24, 1991 Volume 91 : Issue 12

defines Reciprocal Pythagorean sums as,
1/sqrt(a*a + b*b) (*)

He then states the

PROBLEM: Find a division-free algorithm for reciprocal Pythagorean sums
with similar properties to the Moler-Morrison procedure, namely, with fast
convergence and no range-reduction nor overflow/underflow for a "large" set of
pairs a,b of machine numbers...

Some thoughts which might be at least a partial solution to Miel's problem:
Without loss of generality, assume a >= b >= 0, and a > 0. For all c>0, let
d = (a*c)**2 + (b*c)**2. Then 1/sqrt(a**2 + b**2) = c/sqrt(d). This may be a
range reduction, but I think it might still serve the need. One problem is to
compute c so that the calculation of d does not experience overflow or
destructive underflow. c = 1/a or 1/(2*a) should accomplish this, but does
require a division. If even one division is unacceptable, then bit-crunching
using the exponent field of a as data should allow one to generate c of about
the correct size (if a = 1.f*2**e, then c might be 1.0*2**(-e-1)). One then
calculates 1/sqrt(d) iteratively as Meil stated in his communication. If the
convergence speed of Moler-Morrison is desired, then "the usual division-free
Newton-Raphson method for 1/sqrt" could be replaced by the iteration
y = x(i)**2
x(i+1) = x(i) + x(i)*(.875 - ([1.25*d] - [.375*d**2]*y)*y)
which converges cubicly to 1/sqrt(d).

Daniel P. Giesy (
Lockheed Engineering & Sciences Co., Hampton, VA


From: International Linear Algebra Society <MAR23AA%TECHNION@TAUNIVM.TAU.AC.IL>
Date: Tue, 09 Apr 91 08:33:08 IST
Subject: The Toeplitz Lectures in Tel Aviv


ILAS-NET Message No. 110
FROM: Israel Gohberg

Tel Aviv University
Raymond and Beverly Sackler Faculty of Exact Sciences
School of mathematical Sciences

The Nathan and Lily Silver Chair
for Mathematical Analysis and Operator Theory
announcing the
Tel Aviv, April 24 - May 3, 1991

L. de Brange M.A. Kaashoek
Purdue University, Vrije University,
West Lafayette Amsterdam

H.J Landau L.A. Sachnovich
AT&T Bell Laboratories, Communications Institute
Murray Hill Odessa

Operator Theory Days
Dedicated to the Memory of S.G. Mikhlin

April 29 and 30, 1991

with lecturers

A. Atzmon (Tel Aviv University) L. Lerer (Technion)
P. Bleher (Tel Aviv University) V. Lin (Technion)
I. Feldman (Tel Aviv) M.S. Livsic (Ben Gurion University)
I. Gohberg (Tel Aviv University) V. Matsaev (Tel Aviv University)
N. Krupnik (Bar Ilan University) A. Markus (Ben Gurion University)
A. Lazar (Tel Aviv University) B. Paneyach (Technion)

For further information please contact:

School of mathematical Sciences
Tel Aviv University
Tel Aviv 69978
Tel: 03-5450033, 03-5414570


From: Bonnie Yantis <>
Date: Tue, 9 Apr 91 13:04:20 MDT
Subject: Computational Science Workshop at Los Alamos

Summer 1991
Los Alamos Workshop on Computational Science

May 28 - August 23, 1991
Los Alamos National Laboratory
Los Alamos, New Mexico

Deadline for Application: April 19, 1991
Cost: No charge

The Computing and Communications Division and the Advanced Computing
Laboratory invite you to participate in the Summer 1991 Workshop on
Computational Science.

Full-time immersion workshop, designed to provide advanced education for
high performance computing use in computationally-intensive research, will
address science, computing, and collaboration.


* Scientists and engineers in computer-intensive research fields
* Computer scientists and computer engineers
* Educators in science, engineering, and computing
* Graduate students, recent graduates, and others embarking on careers
in computer-intensive scientific research fields
* Graduate students, recent graduates, and others embarking on careers
in computer science and computer engineering

Seminars in computational science, plus work on computing aspects of their
own research, for ten or fifteen scientists, engineers, and educators from
Los Alamos, research laboratories, and academia, balancing research topics
in sciences, engineering, and computer science to promote an
interdisciplinary exchange.

This workshop provides an interdisciplinary environment for scientists,
engineers, and educators. It is centered on seminars on concepts and
issues in computational science with discussions led by local and visiting
lecturers. Participants work on computing aspects of their own research
and learn how to evaluate computational strategies in the context of their
own discipline by exploring the effects of a variety of architectures on
their own application codes. Participants will be drawn from Los Alamos
National Laboratory, research laboratories, and academia, balancing
research topics in sciences, engineering, and computer science to promote
an interdisciplinary exchange.


The full-time workshop will be 12 weeks. Seminars and discussions are
scheduled about a third of the time. The rest of the time is devoted to
aspects of the participant's research. Participants are expected to focus
their efforts on the workshop without the distraction of other projects or
activities outside of their own workshop research.

Seminar Topics

* What is high performance computing?
* Comparative computer architectures and operating systems
* Communications and networks
* Code analysis and optimizations
* Software design
* Scientific computing languages, including Fortran, C, C++, and
* Scientific algorithms, numerical methods, data structures
* Vectorization and parallelization
* Scientific graphics and visualization
* Distributed workstation environments
* Large-scale scientific research and simulations
* Intimate multidisciplinary science collaboration

Cost: No charge.

Deadline for Application: April 19, 1991

Selection of Participants

Ten or fifteen participants will be chosen using the following criteria:

* Working knowledge of Fortran or C and one operating system (e.g.,

* Computer-intensive research topic and a working application program.

* Balance of research topics in sciences, engineering, and computer
science; and the possibility of interdisciplinary exchanges between

* Willingness to serve as consultants or models for others interested in
promoting the integration of high performance computing technology
into research.

Computing Facilities

Each participant will be provided with a workstation in a common office
area, consulting, and computer accounts for a variety of systems:
* Cray machines
* Connection Machine CM-2
* Convex C220
* IBM 3090 600E/VF
* Other advanced architecture machines

Scientific workstations available to participants include Sun, Macintosh
II, IBM RISC 6000, and NeXT. High-performance graphics workstations, such
as Ardent Titan, FPS, and SGI 4D/380 GTX, are also available.

For further information, contact:

Ann Solem or Pat Malone
Group C-2, MS B253
Los Alamos National Laboratory
Los Alamos, NM 87544 USA
telephone: (505) 667-5460
FAX: (505) 667-4361
electronic mail: WPCS.LANL.GOV


From: Heikki Apiola <>
Date: 11 Apr 91 12:30:10 GMT
Subject: Workshop on Symbolic and Numeric Computing, Helsinki

Workshop on Symbolic and Numeric Computation
Helsinki May 30-31, 1991


Helsinki University Computing Centre
The Rolf Nevanlinna-Institute
CSC (Centre for Scientific Computation)


- Computer algebra and some of its applications

- Interaction of Computer Algebra, numerical computation and
scientific visualization

- Applications of Scientific Software and Scientific Computing


The workshop aims to bring together different computational cultures
represented by the symbol algebra, numerical and graphical software and
matrix-vector language communities. We will try to provide a forum for
exchanging ideas and introducing projects that develop or use some
combination of such tools.


Helsinki University Computing Centre
Teollisuuskatu 23
SF-00510 Helsinki
Tel: +358-0-70851
Fax: +358-0-7084441

A tentative list of speakers and demonstrations

James Davenport, University of Bath (UK)
Jarmo Hietarinta, University of Turku (FI)
Norman Thomson, IBM/Winchester (UK)
Ari Lehtonen, University of Jyv{skyl{
Ken Rimey, Helsinki University of Technology
Esko Valkeila, University of Helsinki
Minaz Punjani, University of London
Lasse Holmstr|m, The Rolf Nevanlinna Institute
Alexei Serebrovski, USSR Acad. of Sci
Victor Kistlerov, USSR Acad. of Sci
Heikki Haario, University of Helsinki and the Kemira company
Heikki Apiola, University of Helsinki and Helsinki University of Technology
Pirkka Peltola, Espoo-Vantaa Institute of Technology
Mika Sepp{l{, University of Helsinki and Academy of Finland


Heikki Apiola
Juha Fagerholm
Marko Laine
Esko Valkeila


From: David K. Kahaner <>
Date: 12 Apr 91 15:24:11 GMT
Subject: Kahaner Report from Japan

[David Kahaner is a numerical analyst visiting Japan for two-years
under the auspices of the Office of Naval Research-Asia (ONR/Asia).
The following is the professional opinion of David Kahaner and in no
way has the blessing of the US Government or any agency of it. All
information is dated and of limited life time. This disclaimer should
be noted on ANY attribution. Copies of previous reports written by Kahaner
can be obtained from host using anonymous FTP.
-- Rick Schlichting <>]

Advances in Numerical Methods for Large Sparse Sets of Lin Eqs.
12 April 1991

ABSTRACT. Titles of papers presented at "Advances in Numerical Methods
for Large Sparse Sets of Linear Equations", Keio University, 1 March
1991 are given.

These papers were presented in Japanese. However some papers are
available in English. For information about these contact the organizer,
Dr. Takashi Nodera
Dept of Mathematics
Keio University
3-14-1 Hiyoshi Kohoku
Yokohama 223 Japan
Tel: +81-44-63-1141 ext 3762

The first three papers, about special function properties are from
U-Tsukuba. That group is led by
Professor Yasuhiko Ikebe
Institute of Information Sciences and Electronics,
University of Tsukuba,
Tsukuba City, Ibaraki 305.
Tel: +81 298-53-5535 (O), -5187 (S)

Interesting work on extensions of conjugate gradient are being done by
Dr. Shun Doi
Information Basic Res.Lab.,
C&C Information Tech.Res.Labs.,
NEC Corporation,
4-1-1, Miyazaki, Miyamae-ku, Kawasaki 213, Japan
who is an author of two papers presented here.

PAX is one of the longest running distributed memory projects in Japan
(since 1970s), and one of the few machines in the world for performing
quantum chromodynamics (another is at Columbia). Algorithms for linear
equations on PAX are described by a student of
Professor Yoshio Oyanagi
Institute of Information Sciences
University of Tsukuba
Tennodai 1-1-1, Tsukuba, 305, Japan
Tel: +81 298-53-5518, -5449, Fax: +81 298-53-5206
Oyanagi will be moving to the University of Tokyo this year, but this
address should be usable for a while.

PCG Symposium Keio University (March 1st, 1991)

(1) The Numerical Solution of xJ'_m(x)+HJ_m(x)=0, where
m > -1 and m > M.
Nobuyoshi Asai(College of information Science, University of Tsukuba)

(2) The Numerical Computation of Zero of Bessel Function
of Order < -1
Kouichi Takanashi(College of Information Science, Univ of Tsukuba)

(3) Solving J_k(x) = e and J''_k(x)= 0 for a Given e > 0 and k > 1.
Minoru Harada(College of Information Science, University of Tsukuba)

(4) Evaluating the Bi-CGSTAB Algorithm, Vorst's New Iterative Method
for Nonsymmetric Systems
Hiroshi WATANABE(NEC Scientific Information System Development Corp.)
Shun DOI(C&C Information Technology Research Laboratories, NEC Corp.)

(5) Direct QR Method for finding the Approximate
estimates of large dense symmetric matrices
Yoshitaka Beppu (Shotoku Gakuen Women's College)
Unpei Nagashima (Institute for Molecular Science)

(6) The Effectiveness of Gustafsson's Modification for
Parallel Ordered ILU Preconditioning
Shun DOI(C&C Information Technology Research Laboratories, NEC Corp.)

(7) Modified Incomplete Decomposition Method for a Time Dependent Problem
Seiji Fujino(Institute of Computational Fluid Dynamics)

(8) Gauss Elimination on the Distributed Memory Parallel Computer PAX
Kimio Takahashi(Institute Information Science, University of Tsukuba)

(9) Conjugate Residual Method for Solving Singular Systems
Shaoling Zgang(Institute of Computational Fluid Dynamics)
Seiji Fujino(Institute of Computational Fluid Dynamics)
Yoshio Oyanagi(Institute of information Science, University of Tsukuba)

(10) Reorthoginalization in the Block Lanczos Method
Hiroko IGUCHI ( Institute of Information
Makoto Natori Science and Electronics,
Hitoshi IMAI University of Tsukuba)


Date: Fri, 12 Apr 91 15:06 EDT
Subject: SIAM Conference on Applied Linear Algebra

SIAM Conference on Applied Linear Algebra
September 11-14, 1991, Minneapolis, Minnesota

Dear Colleague:

Just a friendly reminder...... the deadline for submission of
abstracts for presentation at the SIAM Conference on Applied
Linear Algebra is April 19. You can submit your abstracts
(approximately 100 words in length) by

fax to: 215-386-7999

e-mail to:

phone to: 215-382-9800

Include title of presentation, preference (15-minute lecture
format, or poster presentation), full name and affiliation
(speaker and coauthors), and name of conference.

We look forward to your participation. See you in Minneapolis.

Richard A. Brualdi
Conference Chair


From: Steven Lee <>
Date: Sat, 13 Apr 91 09:30:47 CDT
Subject: 2nd Annual Midwest NA day

for the
2nd Annual Midwest NA Day


Location: Champaign-Urbana, IL
Digital Computer Laboratory
1304 W. Springfield Ave, Urbana
Date: Saturday, May 11 1991
8:30AM - 4:30PM

The 2nd Annual Midwest NA Day is scheduled for Saturday, May 11 1991
on the University of Illinois, Urbana-Champaign campus. The first NA
Day was held in April of last year to take special note of the
retirement of Bill Gear from the University of Illinois. This year,
the conference coincides with the May graduation ceremonies in which
Gene Golub is to receive an honorary doctorate from the University.

This is an informal conference with an emphasis on scheduling a
variety of talks from speakers with interests in numerical analysis
and scientific computing. Bill Gear and David Young are two examples
of old friends of Gene's who have already agreed to give talks.

Those who wish to be included on the electronic mailing list for news
on this event (schedule information, travel directions, etc.) should
send email to:

For those who plan to attend and are also interested in giving a
20-minute or 40-minute presentation, please send the title and a brief
abstract of your proposed talk to the e-mail address listed above.

Organizers: Paul Saylor, Robert Skeel, Faisal Saied, Ahmed Sameh,
Michael J. Holst and Steven Lee


Date: Sun, 14 Apr 91 08:32:03 BST
Subject: CERFACS Short Course


(European Centre for Research and Advanced Training in Scientific Computation)

will hold

A three-day advanced short course


An Introduction to Parallel Computing

Monday 22nd April - Wednesday 24th April 1991


Toulouse, France

The course is aimed at scientists in industry and academia who wish to
learn about parallel computing and familiarize themselves through hands-on
experience with a range of parallel computers.

On the first day, some introductory lectures on vector and parallel
architectures will be followed by a more detailed description of the
parallel computers available to students on the course. These will include
a BBN TC2000, an Alliant FX/80 and FX/2812, a TMC Connection Machine CM-2,
an INTEL hypercube, a CRAY 2 and an IBM 3090/VF.

The second day will examine techniques for programming these machines and
tools available to assist in their use. These lectures will be followed by
a discussion of basic numerical algorithms and software.

The final day will address more large scale computing on such
architectures, including the solution of sparse equations, and will provide an
opportunity for students to run their own codes on the machines.

Throughout the course, there will be a strong emphasis on hands-on
experience and it is the intention that students will finish the course
with a basic knowledge of parallelism and how to appreciate, compare, and
use a range of different parallel architectures.

Lecturers include: Amestoy, Arioli, De Roeck (CERFACS), Dongarra (ORNL and
Tennessee), Duff (RAL, CERFACS, and Strathclyde), Jalby (IRISA and Rennes),
Levine (Argonne), Ruiz and Valdettaro (CERFACS).


Dominique BENNETT
42 Ave Gustave Coriolis
31057 TOULOUSE Cedex
Tel : (33) 61 07 96 96
Fax : (33) 61 07 96 13
EMail :


Date: Sun, 14 Apr 91 08:33:40 BST
Subject: Contents: IMA Journal of Numerical Analysis

The contents of the current issue of the IMA Journal of Numerical
Analysis are given below.


The first five papers were presented in the minisymposium on Numerical
Analysis at the IMA Silver Jubilee Conference at Cambridge in September 1989.

C T H Baker and N J Ford Some applications of the boundary locus
method and the method of D-partitions.

M G Cox and P M Harris The approximation of a composite Bezier
cubic curve by a composite Bezier quadratic

I S Duff, N I M Gould, The factorization of sparse symmetric
J K Reid, J A Scott, and indefinite matrices.
K Turner

A Iserles Complex dynamics of convergence

K W Morton and E Suli Finite volume methods and their analysis.

R C Mittal and S Gahlaut High-order finite-difference schemes to
solve Poisson's equation in polar

Gh Adam and A Nobile Product integration rules at Clenshaw-Curtis
and related points: a robust implementation.

J R Dormand, Corrigendum: High -order embedded
M E A El-Mikkawy and Runge-Kutta-Nystrom formulae.
P J Prince (Original paper in Vol 7, 423-430)


End of NA Digest