NA Digest Sunday, May 1, 1988 Volume 88 : Issue 18

Today's Editor: Cleve Moler

Today's Topics:


From: Nick Trefethen <>
Date: Sun, 17 Apr 88 17:35:05 EDT
Subject: Super-Accurate ODE Methods

I have a question about super-accurate numerical solution
of o.d.e.'s; can anyone advise?

Gerald Sussman, a professor in the M.I.T. Dept. of Electrical
Engineering and Computer Science, has built a special-purpose
machine for simulating the long-term evolution of the
outer planets of the solar system. With this device he
and his colleagues have attempted to solve o.d.e.'s to perhaps
unprecedented accuracy: a few percent error over a time integration
of 200,000,000 years, which corresponds to around 20,000,000
orbits of Jupiter (the fastest time scale in the problem).

Here's a sketch of a typical calculation:

Dimension of system of o.d.e.'s: 36
Linear multistep formula: 12th-order Stoermer formula
Step size: about 1/100th of the period of Jupiter
Number of steps: O(10**9) (!!)
Final error: a few percent

My question is, can one do better than to use this 12th-order
Stoermer formula? One hundred points per wavelength seems a
very large number to me, suggesting that a higher-order method
of some kind might be more efficient. But Sussman claims that
in their experience, higher-order Stoermer formulas introduce
such large rounding errors, due to the large oscillatory
coefficients, that the final accuracy is reduced.

Are there other methods for super-accurate o.d.e. calculations
that ought to be considered?

Nick Trefethen

mail: L. N. Trefethen, Dept. of Math., M.I.T., Cambridge, MA 02140
e-mail: OR
phone: 617-253-4986


From: Walter Gander <>
Date: 25 Apr 88 8:37 +0100
Subject: NA-NET report

While in Switzerland Mark Kent wrote a short report on the
NA-NET. There are about 100 hardcopies left over. If you are
interested, please send me your (real) address so we can send
you a copy as long there are available.
- Walter Gander, ETH Zuerich. or


Date: Mon 25 Apr 88 11:31:40-MDT
Subject: Interpolation of Multidimensional Data

I am currently working on a survey paper on interpolation of data
in more than two independent variables. This will be presented at the
upcoming CAGD meeting in Oslo. Of particular interest is the
interpolation of scattered data (i.e., data that exhibit no utilizable
structure in the distribution of the points in the domain). I would
appreciate if you could let me know of any references, algorithms,
interesting problems in this area, and your experience in solving such
problems. In response, I'd be happy to send you a copy of my paper
when it becomes available.

Peter Alfeld, Department of Mathematics, University of Utah, Salt Lake
City, Utah 84112, Tel.: 801-581-6842 or 801-581-6851,



From: Loyce Adams <>
Date: Mon, 25 Apr 88 16:10:40 PDT
Subject: Post-Doc Position at University of Washington

Applications are invited for a Postdoctoral Research Position
beginning Autumn 1988. Candidates should have strong backgrounds
in fluid mechanics and numerical analysis. Applications (with a
resume and three letters of recommendation) will be accepted
immediately and should be sent no later than 15 August 1988 to
Professor W.O. Criminale, Department of Applied Mathematics, FS-20,
University of Washington, Seattle, Washington 98195. Any questions
can be directed to Loyce Adams at na.adams.

The University of Washington is an Equal Opportunity/Affirmative
Action Employer.


Date: Tue, 26 Apr 88 07:46:49 PDT
Subject: Wind Waves

I would appreciate to receive some pointers to the literature on numerical
simulation of the generation of water surface waves by wind.
-- Bas Braams; Plasma Physics Laboratory, Princeton University;


From: Brad Templeton <>
Date: Tue Apr 26 23:51:42 1988
Subject: Fast Floating Point Software for Microprocessors

I'm trying to put together the fastest software math package for
Intel 8086 family computers that can be found. I looked around
for one for a while, and didn't find anything.

I would like some good references on some of these topics, and
possibly some pointers to a potential consultant on these issues.

As you may know, we're talking machines that (without the 8087) have
only 16 bit integer arithmetic. Speed is the primary goal. This
doesn't mean I want "wrong answers, but really fast", but it means that
if I can drop 2 bits of precision and double the speed, I go for it.

I have currently implemented the basic 4 functions with 46 bits precision,
and my implementation seems about 6 times faster than the typical IEEE
emulations out there, which are 64 bits or 80 bits internally, but store
out with 53 bits.

Now it's time to do scientific functions, and possibly do some small
accuracy tuning on the basic functions. Most algorithms for scientific
functions are based on real arithmetic. It seems to me there should be
algorithms out there that use the integer arithmetic and get better
speed. I have heard of CORDIC, but no little of it. I have heard it
requires lots of multi-bit shifts, which the 8086 can't do on a 48 bit
quantity. (The 386 can do a 64 bit quantity, and I'm also interested in

I'm also interested in table driven algorithms for trig and the like which
would be very fast, and still give me a fair number of bits. The Sun
Microsystems course sounded interesting but I can't attend. So I have to
settle for references, photocopies of papers or consulting that I can
find. If this is your alley, mail me or give me a call 800-265-2782 or

(If you know of a really fast package, tell me about that too!)

It seems that the issue of fast FP on a small integer machine is not
a very well covered topic. In most of the world, if you're serious about
fast FP, you get hardware for it. When you have to write general software
for the MS-DOS world, and you can't insist the customer get an 8087, it's
a different story.

Brad Templeton


From: Hans van der Laan <>
Date: Wed, 27 Apr 88 16:30:50 MET
Subject: Eigenvalues of Diagonally Modified Matrices

Can anybody help me with the following problem?
Computing the eigenvalues and eigenvectors of about 4000
complex Hermitian matrices of dimension 150x150, using
F02AXF from the NAG Library, will cost nearly 30 hours of
computing time on a CONVEX Computer. Can this be shortened,
when it is given, that the matrices only differ in values
on the main diagonal?

Hans van der Laan Bitnet: rcdilaa@hdetud1
Delft University of Technology
Computing Centre
Postbus 354
NL-2600-AJ Delft
The Netherlands


Date: Wed, 27 Apr 88 14:25:32 EMT
Subject: Sabbatical Positions at Bergen Scientific Centre

EXPERIENCED mathematicians who wish to consider the possibility of a sabbatical
at BERGEN SCIENTIFIC CENTRE should contact Pat Gaffney or Lothar Reichel at:
Bergen Scientific Centre, Allegaten 36, 5007 Bergen, Norway.

We are interested in talking with applied mathematicians-applied numerical
analysts with at least 5 years experience after Ph.D. The areas of immediate
interest are:


However, scientists with an interest in applying mathematics, modelling,
and numerical analysis techniques are very welcome to apply.



From: Elise Kapenga <dedonker@anl-mcs.ARPA>
Date: Mon, 25 Apr 88 12:38:19 cdt
Subject: Position at Western Michigan University

Notice of faculty position at Western Michigan University,
Computer Science Department
Position: Tenure track position as assistant professor.
Qualifications: Ph.D. In Computer Science or a closely related field.
Preference will be given to applicants with background in numerical
analysis or artificial intelligence. All areas of computer science will
be considered.
Responsibilities: Teaching of graduate and undergraduate computer science
courses, research, and program development.
University: Western Michigan University is a multipurpose university
which enrolls about 20,000 students. It is located in Kalamazoo, a
medium sized city midway between Detroit and Chicago. This is a
pleasant area in which to live with many cultural and recreational
Department: The Computer Science Department currently enrolls about 130
students in the M.S. program and several hundred undergraduate majors.
One of the undergraduate programs is accredited by CSAB. Faculty research
interests include numerical analysis, parallel computing, databases,
AI, simulation, and computer theory. There is a joint Ph.D. program
in Graph Theory and Computer Science offered through the Department of
Mathematics and Statistics.
Facilities: The Academic Computer Center operates a VAX cluster and several
microcomputer laboratories on campus. The Computer Science Department
provides a VAX-750 and currently is enhancing its laboratory facilities
to include 24 MAC-II's, several PC's and 14 Sun workstations. The
university has an Internet connection.
Salary: Salary will be competitive. The academic year is 8 months. Faculty
who teach during either the 2 month Spring session or the 2 month
Summer session receive an additional 22% of their academic year salary.
A full range of fringe benefits, including full TIAA/CREFF contribution,
is provided.
Starting date: Late August, 1988.
Applications: Please send credentials to:
Dr. Donald Nelson, Chairperson
Department of Computer Science
Western Michigan University
Kalamazoo, Michigan 49008 Phone: (616) 387-5646


From: Olavi Nevanlinna <>
Date: Fri, 29 Apr 88 13:09:28 EET
Subject: Numerical Analysis Year in Helsinki


Rolf Nevanlinna Institute shall host a special year concentrating in
numerical analysis during the academic year 1989-90.

Meetings, workshops and/or special courses are organized at least on
the following topics:

- numerics on ODEs
- on integral equations
- on free boundary problems
- supercomputing.

Additional meetings include eg. regular meetings of ECMI and SIAM Nordic

A limited amount of funds has been reserved to support foreign visiting
scientists for periods up to two months.

Rolf Nevanlinna Institute is a national research institute with activities
in both basic and service research in all fields of pure and applied
mathematics. The institute is governed by a board selected jointly by all
mathematics departments of different universities in Finland. The members
of the board represent both the universities and industry.

For more information contact:

Rolf Nevanlinna Institute
Teollisuuskatu 23
00510 Helsinki

or contact me thru na-net: na.nevanlinna

Next announcement thru na-net after summer.
Olavi Nevanlinna


From: Richard Brualdi <>
Date: Thu, 28 Apr 88 12:52:31 cdt
Subject: Happy Birthday to Van Vleck Hall

Van Vleck Hall, which houses the Mathematics Department of
the University of Wisconsin,Madison is 25 years old this
year. An anniversary celebration will be held on May 19-
21,1988. On Saturday afternoon(May 21) of the celebration a
miniconference entitled "Matrix and Combinatorial Theory-25
years at VanVleck" has been organized by Richard A. Brualdi
and Hans Schneider. The speakers are many of their former and
present Ph.D. students and colleagues. Everyone is invited to
attend the miniconference; those people attending the SIAM
conference on Applied Linear Algebra in Madison beginning on
the following Monday and who are arriving in Madison early
for that conference may wish to attend the miniconfernce.


Matrix and Combinatorial Theory-25 years at Van Vleck

Saturday, May 21, 1988, 1:00-5:30 pm
Van Vleck Hall, University of Wisconsin-Madison

Chairman of Session: David Carlson

1:00-1:15 Shmuel Friedland, University of Illinois @ Chicago:
Even cycles in directed graphs.
1:15-1:30 David Saunders, University of Delaware: Extremely
fast computation of matrix canonical forms.
1:30-1:45 George Dinolt, Ford Aerospace Research: Trust, but
1:45-2:00 Wayne Barrett, Brigham Young University: Spectral
properties of a (0,1)-matrix related to Mertens' function
2:00-2:15 Dan Pritikin, Miami University: On packing trees
into half-complete graphs.
2:15-2:30 Jeffrey Ross, Bell Communications Research: Systems
engineering at Bellcore.
2:30-2:45 Suk Geun Hwang, Taegu University-Korea: Some
nontrivial permanental mates.
2:45-3:00 Bit-Shun Tam,Tamkang University and University of
Wisconsin: On distinquished eigenvalues of a cone-preserving

3:00-3:30 COFFEE BREAK

3:30-3:45 Robert Wilson, Ford Aerospace Research: Proofs in a
relativistic world.
3:45-4:00 T.S.Michael, University of Wisconsin and Louisiana
State University: The parsimonious Pasadena algorithm-The
true story.
4:00-4:15 James R. Weaver, University of Western Florida:
Reflexive states of a Markov chain.
4:15-4:30 Han-Hyuk Cho, University of Wisconsin: Indexes in
the Hall matrix semigroups.
4:30-4:45 Volker Mehrmann, University of Bielefeld:
Qualitative controllability for pairs of matrices (A,B).
4:45-5:00 Chi-Kwong Li, University of Wisconsin: Matrices and
their c-numerical ranges.
5:00-5:15 G.M.Engel,Linkabit: Matching problems in
5:15-5:30 Paul Terwilliger,University of Wisconsin: A
generalization of the Bose-Mesner algebra of an association


End of NA Digest