NA Digest Sunday, March 26, 1995 Volume 95 : Issue 13

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

Submissions for NA Digest:

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Information about NA-NET:

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URL for the World Wide Web: -------------------------------------------------------

From: G. W. Stewart <>
Date: Fri, 24 Mar 1995 08:49:18 -0500
Subject: History of Flops and Errors

I am writing a multivolume Survey of Matrix Computations, due to
appear at the millennium. I have a couple of queries in connection
with the chapter on Matrices and Machines.

* Who coined the word flop, and when?

* Some time ago there was a Wall Street Journal article about
chopping error depressing an index on the Canadian Stock
Exchange. Can anyone point me to the source?

Pete Stewart


From: William Behrman <behrman@sccm.Stanford.EDU>
Date: Mon, 20 Mar 1995 19:48:59 -0800
Subject: Software Sought for Large-scale, Unconstrained Optimization

I would appreciate any advice the community has on software for solving
large-scale, unconstrained optimization problems.

For each problem to be solved, I have routines to calculate the
objective function, the gradient, and often the product of the Hessian
with any given vector. I need software that requires only O(n) storage.

Thank you very much,

William Behrman
Scientific Computing


From: Jose Alberto Cuminato <>
Date: Tue, 21 Mar 95 11:13:32 EST
Subject: Software for Non-linear Parabolic Equations

I am looking for a public domain FORTRAN code to solve the parabolic non-linear
coupled pair of equations:
u_xx = u_t + F(u) + G(u,v,v_t)
v_xx = v_t + H(v) + I(u,v,u_t)
where F and H are non-linear but G and I are linear. The boundary conditions
are periodic, and I am interested in the long time behaviour of the solution.
Specifically, i am trying to show that the solutions syncronize independent of
the initial conditions.
J. A. Cuminato


From: Lianhua Lu <>
Subject: Inverse of Special Matrix


I'm looking for a fast algorithm for the inverse of the matrix (looks like

                 2    3                2    3
[ c1 c1 c1 ] [ d1 d1 d1 ]
[ 2 3 ] [ 2 3 ]
[ c2 c2 c2 ] - [ d2 d2 d2 ]
[ 2 3 ] [ 2 3 ]
[ c3 c3 c3 ] [ d3 d3 d3 ]

for 3 x 3 case)

Any pointers would be appreciated.

Thanks in advance,
Lianhua Lu
Dept. of Math., Arizona State Univ.



From: Donglei Chen <>
Date: Fri, 24 Mar 1995 4:37:54 -0500 (EST)
Subject: Root Finding with Complex Function

Hi, I am seeking for a subroutine that can be used for finding roots of an
arbitrary COMPLEX function. Is there anyone who can tell me where I can get

Thanks a lot in advance.

Donglei Chen
Department of Physics
The University of Western Ontario
London, Ontario, Canada
N6A 3K7



From: Jeff Cash <>
Date: Tue, 21 Mar 1995 10:11:02 GMT
Subject: New Boundary Value Code in Netlib

New Boundary Value Code in Netlib

A new code is available from netlib for the solution of boundary value
problems. It is mainly designed to solve stiff two-point boundary
value problems, including singular perturbation problems, and uses
mono-implicit Runge-Kutta methods in a deferred correction framework.
The algorithm and performance of the code are described in:
Cash and Wright (1991), A deferred correction method for
nonlinear two-point boundary value problems, SIAM Journal on
Scientific and Statistical Computing 12, 971-989.
The Fortran 77 source code can be obtained from netlib by sending
the message
send twpbvp.f from ode
The user manual is a LaTeX file, which can be obtained from netlib
by sending the message
send twpbvp.tex from ode
Any comments (good or bad), reports of experience, or inquiries about
extensions will be gratefully received by J. R. Cash, Department of
Mathematics, Imperial College, London, United Kingdom,


From: Joe Grcar <>
Date: Wed, 22 Mar 95 11:12:20 -0800
Subject: Suggestion for Recent Contents Publication

It seems evident to me that there is a need for a
publication that lists the recent contents of
Numerical Analysis journals. Would some professional
organization or publisher please take up this suggestion?

My model for this is the "Heat Transfer - Recent Contents"
published by the American Socity of Mechanical Engineers.
This bimonthly newsletter simply lists the titles, authors,
and page numbers of all the articles appearing in the
roughly 30 international journals that deal with heat
transfer. It is quite convenient to read through the list,
check off the articles that look interesting, and then
head over to the library to get them--the heat transfer
literature has many practical examples of numerical analysis,
by the way.

I note that roughly half the messages in the NA Digest
are simply lists of journals' contents. These, and perhaps
also lists of conferences, would be more conveniently
displayed in a uniform format in a publication such as
the heat transfer people have. The Math Reviews are not
the same thing, and the Current Contents publications
focus more on the physical sciences than on mathematics.

Regards, Joe Grcar


From: Leonid Kalachev <>
Date: Wed, 22 Mar 1995 16:23:58 -0700 (MST)
Subject: New Book on Singular Perturbations

I have recently published a new book on singular perturbations
and their applications with SIAM.

Title: The Boundary Function Method for Singular
Perturbation Problems
Authors: Adelaida B. Vasil'eva, Valentin F. Butuzov,
and Leonid V.Kalachev
221 pages, hard cover, published in February 1995.

Those of you who are interested in this field may find the book
very helpful.

Please feel free to contact SIAM for further information:

Leonid Kalachev


From: Peter Deuflhard <deuflhard@ZIB-Berlin.DE>
Date: Fri, 24 Mar 95 14:16:39 +0100
Subject: New Book on Numerical Analysis

The first volume of the Numerical Analysis book by Peter Deuflhard and
Andreas Hohmann, which had been available and well-accepted within the German
speaking community for some years, is now available in English translation
as a De Gruyter Textbook (paper back $39.95).
The rather elementary presentation of the material has been made with a strict
view to the needs of Computational Science. Important concepts of
modern numerical analysis are illustrated with the simplest type of problem to
which they are applicable. Among the topics, which are not standard, are a
rather simple treatment of error analysis (avoiding the usual "epsilon-battle"),
affine invariant Newton techniques (for beginners), computational aspects of
three term recurrences (the infinite dimensional analogue of orthogonal
transformations), and adaptive Romberg quadrature as well as adaptive multigrid
quadrature for definite integrals. The main aim of the book is the development
of algorithmic thinking and intuition.
The book addresses students of mathematics and the natural sciences, as well as
applied mathematicians and computational scientists in academia and
industry. Required prerequisites are a basic knowledge of undergraduate
Linear Algebra and Calculus.

Those interested to learn more about the scope of the book may have access
via the following:

The book is available from Walter de Gruyter & Co. (Berlin, New York).

Peter Deuflhard, ZIB Berlin.


From: Paul Nevai <>
Date: Thu, 23 Mar 1995 19:18:47 -0500 (EST)
Subject: Contents of Journal of Approximation Theory Available via WWW

It is our great pleasure to announce that we have made available the Table of
Contents of all issues of J. Approx. Theory via WWW.


JAT home page:

Enjoy (and spread the word)...

We are grateful to Carl de Boor (, his sister Elisabeth,
and to Lyn Radcliff ( for making the Table of
Contents of J. Approx. Theory available. If you find this information useful,
please send a memo of appreciation to them.

Paul Nevai and Allan Pinkus

If you have any comments to make, please don't hesitate to contact me

Paul Nevai
Department of Mathematics
The Ohio State University nevai@ohstpy.bitnet
231 West Eighteenth Avenue 1-614-292-3317 (Office)
Columbus, Ohio 43210-1174 1-614-292-5310 (Answering Machine)
The United States of America 1-614-292-1479 (Math Dept Fax)


From: Anne-Marie De Meyer <>
Date: Tue, 31 Jan 95 11:13:41 UTC+0100
Subject: Sup'Prize for IBM Parallel Platforms

in conjunction with the Sup'Eur conference
Prizes worth 15,000$

What is Sup'Eur?

"Sup'Eur is the association of European users of high-performance
computing on IBM platforms.
The goal of Sup'Eur is to facilitate the usage of IBM high-performance
computers (SPx machines and RISC clusters) and software for the
academic, research and industrial environments.
The group seeks to foster the exchange of ideas and experiences,
to solve problems, to discuss solutions, to submit requirements to IBM
and to keep up to date with the latest in HPC.
Activities include an annual conference, an electronic discussion list,
workshops, meetings with IBM, call for experiences."

What is the Sup'Prize?

It is a contest, sponsored by IBM Scientific, Technical and Education
Industries, with the following objectives:

o To encourage the development of expertise in scalable parallel
and cluster computing on IBM RISC based systems throughout the
scientific and technical community in EMEA (Europe, Middle
East and Africa).

o To encourage and recognise software excellence in the exploitation of
IBM POWER Parallel scalable systems and IBM RISC System/6000 cluster
technology by presenting annual Achievement Prizes, worth
15,000 dollars, offered by IBM.

o To provide an opportunity for direct informal communication on topics
related to scalable parallel computing on IBM systems through
the annual Sup'Eur conference.

o To provide an open forum for the exchange of ideas, experience,
techniques and solutions to problems related to scalable parallel
computing and workstation clustering on IBM AIX platforms.

A postscript version with the rules of this contest and enrollment form
is available by anonymous ftp from
in the directory /pub/
The filename is
Anne-Marie De Meyer
Computing Centre
K.U. Leuven


From: M. Bartholomew-Biggs <>
Date: Tue, 21 Mar 1995 13:17:13 +0000 (GMT)
Subject: Optimization Course at University of Hertfordshire


Full-time M Sc in Optimisation

This new course, running under the Credit Accumulation and Transfer
Scheme (CATS), will be offered from September 1995 and consists of a
taught component (running from September to June) leading to a
Postgraduate Diploma. In order to obtain the M Sc students must also
complete a project between July and late September.

Building on the expertise of the Numerical Optimisation Centre, the
course involves comprehensive study of methods of Linear and Nonlinear
Programming. In addition, students must choose from a number of
supporting courses in aspects of Mathematical Modelling.

This course is also available in part-time mode, alongside other
part-time M Sc programmes in Numerical Computation, Mathematical
Modelling and Mathematical Studies. More details and application forms
for any of these schemes can be obtained from:
Dr M. Bartholomew-Biggs, Division of Mathematics, University of
Hertfordshire, College Lane Hatfield AL10 9AB, England


From: Venkat Sastry <>
Date: Fri, 24 Mar 95 9:58 BST
Subject: Fortran 90 Course

Introduction to FORTRAN 90
9--11 May 1995

This 3 day course is an introduction to the new Fortran standard. Suitable
for non-Fortran programmers, it covers almost all new features of the

Extensive hands-on work uses the NAG F90 compiler. Also available are the
new NAG fl90 library of numerical procedures specially written to exploit
Fortran 90 features, and NAGware f90 tools, a set of QA and program
transformation tools that are an essential companion to the serious Fortran
90 programmer.

Some experience in scientific software development is a prerequisite.
Knowledge of Fortran 77 is not required as Fortran 90 is introduced from the
beginning. 'Fortran 90 Explained' by Metcalf & Reid and comprehensive
course notes are provided.

Course Leaders:

Dr John Pryce, Dr Venkat Sastry (RMCS)
Prof John Reid (Rutherford Appleton Laboratory), international expert on
Fortran 90 and author of course text.

For further details and a registration form contact:

Short Course Administrator (SEES)
Cranfield University
Royal Military College of Science
Shrivenham, Swindon
Wilts SN6 8LA.

Tel: (0793) 785253 Fax:(0793) 782146
Email: {sastry,pryce}


From: Jose Alberto Cuminato <>
Date: Mon, 20 Mar 95 15:03:55 EST
ubject: Position at University of Sao Paulo, Brazil

Vacant Position In Numerical Analysis/ Scientific Computing

Applications are invited for this position at the University of Sao Paulo,
at Sao Carlos. We are particularly interested in people with a good background
in CFD and are willing to learn Portuguese for teaching in about one year from
starting. More information is best obtained via e-mail to the address:
or to the Postal address:
J. A. Cuminato
Caixa postal 668
13560-970 Sao Carlos - SP


From: John Dennis <>
Date: Tue, 21 Mar 95 14:28:10 CST
Subject: Postdoctoral Position at Rice University

Postdoctoral Position at Rice University:
The Optimization Project of the Center for Research on
Parallel Computation
has a possible postdoctoral position in applications and
algorithm development for large scale numerical nonlinear
programming. In addition to a research interest in this
area, it is crucial that the applicant be a good
writer and speaker and have an interest in modern software
design and implementation. The position will be under
the direction of John Dennis and will be a research
appointment in the Department of Computational and Applied
Mathematics at Rice University in Houston, Texas.
Contact John Dennis,,
immediately if you are interested in at least one year
in this position.


From: Brent Lindquist <>
Date: Wed, 22 Mar 95 14:38:30 EST
Subject: Postdoctoral Positions at Stony Brook

State University of New York at Stony Brook
Department of Applied Mathematics and Statistics

The department expects to have postdoctoral positions in computational
applied mathematics available for the 1995-96 academic year.
Qualified candidates should have computational experience in one
or more areas of: fluid dynamics, parallel computing, hyperbolic
conservation laws, flows in elastic and plastic media, and flows in
porous media.

Applicants should send vita, descriptions of research interests, and
three recommendation letters to: James Glimm, Chair, Department of
Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook,
NY 11794-3600.

SUNY at Stony Brook is an equal opportunity/affirmative action
employer and educator and encourages applications from women and


From: Ellis Cumberbatch <>
Date: Wed, 22 Mar 1995 14:15:37 -0700 (PDT)
Subject: Postdoctoral Position at Claremont Graduate School

McDonnell Douglas Aerospace, Long Beach/
Claremont Graduate School

Applications are invited from recent math sciences Ph.D.'s
for a two-year post-doc position jointly funded by the NSF Mathematical
Sciences University-Industry Post-doctoral program and McDonnell
Douglas Aerospace. The mentors are Tuncer Cebeci from Douglas
and Ellis Cumberbatch from Claremont.

The research will involve studies in multidisciplinary
design analysis and optimization; special emphasis will be placed
on aerodynamics, and structures. Candidates should have strong
backgrounds in aerodynamics, grid-generation, structures and high
speed computing.
A vita and the names of three references should be sent to
Ellis Cumberbatch, Mathematics Department, Claremont
Graduate School, Claremont, CA 91711.
Phone 909-621-8080. Email: CUMBERBE@CGS.EDU

CGS is an affirmative action/equal opportunity employer and
encourages applications from minorities and women.


From: David EKCHIAN <>
Date: Thu, 23 Mar 95 17:17:26 +0100
Subject: Research Positions at ETH, Zurich

Swiss Federal Institute of Technology Zurich
Inst. Structural Engineering

Employment offer for FE-specialists

Within the research group lead by Prof. Dr. E. Anderheggen at the Institute
of Structural Engineering of the Swiss Federal Institute of Technology (ETH)
in Zurich, three positions will open this year:

1. A teaching-assistant position with the possibility of doing research work
in the field of structural engineering, especially in relation to the finite
element method and finite element program development.

2. A full-time research-associate position for a new project financed by the
Swiss National Science Foundation on "Numerical Simulation of the Creeping
Deformation, Temperature Distribution and Water Transport in a Phase Changing
Snowpack" in collaboration with the Swiss Federal Institute for Snow and
Avalanche Research. A new finite-element program written in C or C++ for the
numerical simulation of the physical behaviour of snow and avalanches is to
be developed. This demanding project will involve several active finite
element research fields including the numerical treatment of large strains,
sliding contact, phase change and flow in unsaturated porous media.

3. A half-time research-associate position for a project entitled
"Three-Dimensional Numerical Simulation of Elastic and Plastic Stress Wave
Propagation in Contacting, Impacting and and Penetrating Solids" in
collaboration with the well-known company HILTI. A new finite-element program
capable of simulating the penetration of steel nails into steel or concrete
substrates is to be developed. The program will be written in C++ for
distributed memory parallel processors. The main research areas in this
project are numerical treatment of stress wave propagation and
contact/impact, parallel processing and strain-rate dependent material

Expertise in finite element analysis and programming (but much can learned
here) as well as interest in theoretical work is required. The ideal
canditates will have a strong background in structural mechanics. Some
knowledge of the german language would help, but is not a perequisite.
All 3 positions provide the opportunity to earn a Ph.D. degree. Acceptance
exams and at least four years are generally needed to reach this goal.
Swiss salaries are adequate.

Appliants are requested to send all relevant personal information to the
reply addresses given below. Letters of recommendation should be included.
Of course, a personal interview in Zurich would be ideal.

Reply adresses:

Prof. Dr. E. Anderheggen
Institut fuer Baustatik und Konstruktion
CH-8093 Zurich

E-mail inquiries are to be addressed to

Dr. P. A. Bartelt
Swiss Federal Institute for Forest, Snow and Land Research
CH-8903 Birmensdorf

Telephone : (Switzerland) + 1-739-2470


From: Panos Pardalos <>
Message-Id: <>
Subject: Contents, Journal of Global Optimization

Contents, Journal of Global Optimization
Volume 6, No. 2, March 1995

THOMAS A. FEO and MAURICIO G. C. RESENDE / Greedy Randomized
Adaptive Search Procedures

VARBRAND / The Minimum Concave Cost Network Flow Problem with
Fixed Numbers of Sources and Nonlinear Arc Costs

O. L. MANGASARIAN / The Linear Complementarity Problem as a
Separable Bilinear Program

D. MOTREANU and P. D. PANAGIOTOPOULOS / Nonconvex Energy
Functions, Related Eigenvalue Hemivariational Inequalities on
the Sphere and Applications

LE D. MUU, BUI T. TAM, and S. SCHAIBLE / Efficient Algorithms
for Solving Certain Nonconvex Programs Dealing with the
Product of Two Affine Fractional Functions

DING-ZHU DU and DEAN F. KELLEY / On Complexity of Subset
Interconnection Designs

W. B. LIU and C. A. FLOUDAS / Convergence of the (GOP)
Algorithm for a Large Class of Smooth Optimization Problems

PANOS M. PARDALOS / An Open Global Optimization Problem on the
Unit Sphere


End of NA Digest