NA Digest Friday, June 14, 1996 Volume 96 : Issue 23

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

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From: Ulla Miekkala <>
Date: Tue, 11 Jun 96 15:07:00 +0200
Subject: Hans Munthe-Kaas Receives Froberg Prize

The Carl-Erik Froberg Prize for young Nordic authors was awarded on
June 6th, 1996, in the 22nd Nordic Congress of Mathematicians held
in Lahti, Finland, to

Hans Munthe-Kaas, Norway
for his excellent article
"Lie-Butcher theory for Runge-Kutta methods".

The Prize, 25000 Dkr, is given in even numbered years to a young
Nordic author of a paper published in BIT Numerical Mathematics.
The Prize has previously been given as follows:

1994 Ulla Miekkala, Finland
1990 Per Christian Hansen, Denmark
1988 Gunilla Kreiss, Sweden.

The prize committee consisted of members of the editorial board of BIT.

Olavi Nevanlinna


From: Ilse Ipsen <>
Date: Thu, 6 Jun 1996 19:32:22 -0400
Subject: Numerical Linear Algebra Preprints Available

The following papers are available in postscript format from:

S.C. Eisenstat and I.C.F. Ipsen: Relative Perturbation Results for
Eigenvalues and Eigenvectors of Diagonalisable Matrices

I.C.F. Ipsen: Computing an Eigenvector with Inverse Iteration

J.M. Banoczi, N. Chiu, G.E. Cho, and I.C.F. Ipsen: The Influence of the
Right-Hand Side on the Accuracy of Linear System Solution

-- Ilse


From: Isaac Harari <>
Date: Mon, 10 Jun 1996 19:32:40 +0300
Subject: Israel Association for Computational Methods in Mechanics

The WWW home page of the Israel Association for Computational Methods in
Mechanics (IACMM), an affiliate of the International Association for
Computational Mechanics (IACM), is accessible via URL

We invite the participation of the computational community within Israel
and abroad.

Isaac Harari
Department of Solid Mechanics, Materials and Structures
Tel Aviv University
69978 Ramat Aviv, ISRAEL

Phone: +972-3-640-9439
Fax: +972-3-640-7617


From: Tom Hoffend <>
Date: Tue, 11 Jun 1996 08:11:33 -0500
Subject: Adaptive Grid Generation

I am searching for information, in particular major references and/or
review papers and books, concerning method/strategies/analysis of
adaptive grid generation for finite difference methods for systems of
reaction/advection/diffusion equations. I am looking at a class of
problems where very sharp fronts develop.

I am starting with some references from the chemical engineering
literature and would like to find out what is happening in the applied
mathematics community. Thank you.

Tom Hoffend

Thomas R. Hoffend Jr.
3M Company
3M Center Bldg. 201-BN-31
St. Paul, MN 55144-1000


From: Rajiv Kamilla <>
Date: Tue, 11 Jun 1996 16:51:10 -0400 (EDT)
Subject: Maximum Likelihood Estimation of Transition Probabilities


Hello -- Any suggestions or advice with respect to the problem
indicated below would be immensely appreciated.
Thank you very much in advance.

Let us assume that there are N particles which populate
n states (n << N). These n states have different degrees of
stability of occupation and we are interested in estimating the
T_{n x n} matrix where T_{ij} ( i and j run over all indices
1 to n) indicates the transition probability from state i to state j
(viz. T_{ij} == Probability Transition from i --> j )

The (in)stability of occupation of state i (for all i=1,2,3...n)

S_i = \ (T_{ij}) (j not equal to i)

Now let's say we have a time series that indicates
the different states occupied by each of the N
particles as a function of time.

What are the relevant parameters one should calculate
(with the associated likelihood indicators) that would
provide an unbiased estimate of the T_{ij} (i,j=1,2,...n)?
Can any Maximum Likelihood analysis be associated in the
estimation of T_{ij} ?

The time series is finite and large N or large time
approximations are not immediately obvious or valid.

The T_{ij} would need to be associated with a confidence

Can a optimal time of transition t_{ij} be associate
with the tranisition T_{ij} ?

Rajiv Krushna Kamilla email address:
Physics Dept. Phone: (516) 632-8172(work)
SUNY@Stonybrook (516) 331-3978(home)
NY-11794-3800 WWW:


From: Frank D Uhlig <>
Date: Thu, 13 Jun 1996 09:13:59 -0500 (CDT)
Subject: Query on the Square Root Function


How many multiplications/divisions does evaluating one real (or complex)
square root sqrt(a) take ?

How is it done at the state of the art level?

There are several Newton iteration algorithms available.
The quadratically convergent one takes 2 mult/divides and converges in 5
to 13 iterations for 0 <= |a| <= 2 with my initial 'dumb guess' of x_0 = a.

The cubically convergent one takes 5 mult/divides, converging in 3 to 7
iterations with the same dumb start x_0 = a.

quadratic Newton iteration for x = sqrt(a):
x_{n+1} = (x_n + a/x_n)/2

cubic Newton iteration:
x_{n+1} = (x_n*(x_n^2 + 3*a)/(3*x_n^2 + a)

Am I correct to give a square root the mult/divide equivalent of around
18 'old' flops?
Am I correct to give the quadratic one the nod? (about twice as slow, on
average, but 2.5 times cheaper in each step.)

I realize that the initial guess x_0 is a flop saver; how can one
judiciously guess?
Can one use a hybrid method: start with quadratic Newton, followed by
a cubic final afterburner?

What about square roots of complex numbers? I noted similar convergence
of the same iterations above over the complexes. Any better schemes there?
Initial guesses?

Incidentally, MATLAB seems to use the quadratic method; my iterative
results in quadratic mode seem to agree more closely with the MATLAB
square root function than with those from the cubic method.

Thanks to all that can help me with this; it must be old hat for someone
out there, but not for me ...

Frank Uhlig


From: Cathrine Mavriplis <>
Date: Fri, 7 Jun 1996 15:33:36 -0400 (EDT)
Subject: Postdoctoral Position at George Washington University


Center for Combustion and the Environment
The George Washington University
Washington DC

The newly-formed Center for Combustion and the Environment at the
George Washington University has an opening for a Postodoctoral
Research Associate in the area of simulation of combustion
processes. The immediate objective is for the candidate to perform
spectral element simulations of time-varying laminar diffusion flames
to investigate the effect of vortex-chemistry interaction on pollutant
production. The ideal candidate would have significant experience in
developing computational fluid dynamic algorithms and have some
knowledge of combustion, including familiarity with the CHEMKIN
computational package. This position requires a Ph.D. in Engineering
or the Sciences. The candidate will also be expected to act as a
liaison between the computational research group of the center housed
in Mechanical Engineering and the experimental research group of the
center housed in Chemistry. Additional experience in parallel
programming would be considered an asset.

Interested persons should send their resume to:

Prof. C. Mavriplis
801 22nd ST NW
George Washington University
Washington DC 20052

or by fax to:
(202) 994-0238

or by email to:

GW is an Equal Opportunity Employer


From: Olivier Hardy <>
Date: Mon, 10 Jun 1996 09:15:22 -0500
Subject: Position at Computational Mechanics, Austin, Texas

Computational Mechanics Co., Inc. (COMCO), is a small high-tech
engineering consulting and software development company based in
Austin, Texas. COMCO specializes in application of adaptive finite
element methods in many areas of computational mechanics including
fluid and solid mechanics.

COMCO has an immediate opening for an application development engineer
in the areas of computational fluid dynamics (CFD) and numerical heat
transfer. The successful candidate must have at least a MS in engineering
with strong background in CFD and heat transfer applications, must have
good knowledge of finite element methods and variational formulations
as applied to CFD and must be proficient in C programming language.
Self motivation, effective communication skill and team work spirit are
also essential.

In addition, multi-disciplinary CFD application experience, familiarity with
finite volume/finite difference techniques, graduate level knowledge of
continuum mechanics and linear algebra, hands-on experience with commercial
CFD and mesh generation codes, and one to two years of relevant industry
experience will be pluses.

Please send resumes to:

Attn: CFD-Resumes
The Computational Mechanics Co., Inc. (COMCO)
7701 N. Lamar, Suite 200
Austin, Tx 78752
Fax: 512 467 1382

Resumes using plain text may also be sent via e-mail to
"". No phone calls please.

Additional information on COMCO may be found on the internet at


From: Pekka Neittaanmaki <>
Date: Tue, 11 Jun 1996 12:58:30 +0300
Subject: Position at University of Jyvaskyla, Finland

Professorship in Telecommunication

The University of Jyvaskyla in cooperation with Telecom Finland seeks
Professor position for its new Telecommunications Program (TP) for
teaching, research and development. The successful candidate must
demonstrate a strong commitment to graduate education and research
projects in Master School in Information Technology. Additionally,
he/she is expected to develop a skillful research program in partnership
with Telecom Finland.

Fields of Teaching/Research/Development

The professorship position is eligible in one of the following areas in
telecommunications networks design:

Mathematical Modelling of Communication Systems
Digital and Adaptive Signal Processing
Electronics and Hardware Design of Communication Systems
Network Management and Computer Controlled Interfaces
Database Processing of Automated Exchanges
Intelligent Networks and Mobile Phone Networks

Although applications are welcome from anyone who holds a Ph.D. in
Telecommunication, Computer Science, Electrical Engineering or Computer
Systems Engineering, the Telecommunications Program has a particular
interest in candidates who are qualified in electronics and telecommunication

The actual staff of the Telecommunications Program is expected to offer
M.S. and PhD degrees in telecommunication systems. More information about
the city, the university and the department can be found in the WWW

Applicants should submit a detailed resume and the names of at least
three references to: Professor Pekka Neittaanmki, Department of Mathematics,
University of Jyvaskyla, FIN-40351 Jyvaskyla, FINLAND, Tel. (358)-41-602732,
Fax. (358)-41-602731, Email:

Applications must be received by 14th June, 1996.


From: Hans Munthe-Kaas <>
Date: Wed, 12 Jun 1996 10:06:20 +0200
Subject: Position at University of Bergen, Norway

RESEARCHER - Object oriented numerics/ seismic modeling

At Department of Informatics, University of Bergen, Norway, a position
as a researcher is available in the period September 1. 1996 to July 1.
1997. There are possibilities for continuation after this date.

The applicants should hold a Ph.D. or master degree, in either
mathematics or computer science.

The person to be employed will work in a project related to seismic
modeling, financed through the norwegian research council and several oil
companies. The goal is to develop integrated tools for geological,
geophysical and seismic modeling, and involves researchers from different
fields and from the industry. The particular task for this position is the
development of code for modeling elastic waves on sequential and parallel
computers. The code is build around the SOPHUS library, which is an object
oriented C++ library for solving general tensor field equations being developed
as a part of this and other projects.

In the evaluation of the applicants, we will emphasize experience in object
oriented program design, and a good background in numerical analysis or other
areas of mathematics.

The salary depends on qualifications and experience. For candidates holding a
master degree it is in the range 206,000 - 280,000 NKr, and for Ph.D. in
the range 269,000 - 312,000 Nkr. (6.6 Nkr ~ 1 US $).

Applicants should send their vitae and references by _email_or_fax_
to the below address _as_soon_as_possible_. Send verified copies in paper
mail. Applications received after June 27. will probably not be considered.

Paper mail:

Associate Professor
Hans Munthe-Kaas
Department of Informatics
University of Bergen
N-5020 Norway

Fax: +47 55584199


From: Rick Palmer <>
Date: Thu, 13 Jun 1996 16:34:02 -0400
Subject: Position at Beam Technologies, Ithaca, NY

Title: Numerical Software Development Specialist.
Start Date: Immediately, 5/13.
Location: Ithaca, NY.
Employer: BEAM Technologies, Inc.

Responsibilities: Develop components of innovative software tool for
partial differential equation simulation (PDESolve); develop
applications using PDESolve; support PDESolve users developing
applications (both inside and outside of BEAM); Participate in
scientific research projects involving the development of new
PDE-based algorithms and applications.

Qualifications and Experience:
Ph.D. in applied math. or engineering with at least two
years of experience.
Solid background in finite elements as witnessed by writing at least
one complex nonlinear PDE simulation code.
Excellent computer and software development skills.
Excellent numerical analysis skills.
At least two years of experience developing numerical software in C++.
Proven ability to work in a team.
Excellent people, communication, and instructional skills.
Motivation and desire to help users.

Salary and Benefits:
Competitive salary up to $60K commensurate with experience
and qualifications.
Full benefits including 401K plan, health, vacation, etc.
Stock option plan.

Send resume to:
c/o PDE search
BEAM Technologies, Inc.
110 N. Cayuga St.
Ithaca, NY 14850


From: K. Chen <>
Date: Wed, 12 Jun 1996 17:05:30 +0100
Subject: PhD Studentship at Liverpool, UK

Applied Mathematics Division
Department of Mathematical Sciences
The University Of Liverpool

PhD Studentships in Computational Mathematics (on-line application)

A Liverpool University Studentship is available for a prospective
PhD student to be supervised by Dr Ke CHEN (with collaborations)
email =
beginning from October 1996. The PhD would be in the area of numerical
solution of partial differential equations,
investigating adaptive meshing and other related CFD questions.
Applicants should be currently enrolled in, or have completed, the final
year of an undergraduate degree in Mathematics. An MSc would be an
advantage, but is not required. As well as an interest in
Computational Mathematics (Numerical Analysis),
applicants should have a willingness to work on both analysis and
practical problems. Applications include circuit breakers,
semiconductor diffusion or wave scattering.


From: (Iain Duff)
Date: Fri, 7 Jun 96 17:00:16 BST
Subject: Contents, IMA J. Numerical Analysis


Meerbergen K. and Roose D
Matrix transformations for computing rightmost eigenvalues of large
sparse non-symmetric eigenvalue problems.

Girault V and Lopez H
Finite-element error estimates for the MAC scheme

Jimack P K
Optimal eigenvalue and asymptotic large-time approximations using the
moving finite-element method.

Milner F A and Park E-J
Mixed finite-element methods for Hamilton-Jacobi-Bellman-type equations.

Al-Zanaidi M, Grossmann, C., and Voller R L
Monotonous enclosures for the Thomas-Fermi equation in the isolated
neutral atom case.

Aston P J and Sittampalam A G
Numerical methods for steady-state mode interactions.


From: Carlos A. de Moura <>
Date: Mon, 10 Jun 96 10:04:37 EST
Subject: Contents, Computational and Applied Mathematics

Ed: Sociedade Brasileira de Matematica Aplicada e Computacional-SBMAC
and Birkhauser Boston
Editors: Jim Douglas Jr.; C.S. Kubrusly; C.A. de Moura

Mat.Aplic.Comp. \ Comput.Appl.Math. 15(1), 1996

Martel,Y (1-17):

Ben-Yu,G; Xun,L; Vazquez,L (19-36):

Banks,SP; Moser,A; McCaffrey,D (37-54):

Cash,JR; Silva,HHM (55-75):

Thompson,M; Rubio,O (77-94):


End of NA Digest