**Today's Topics:**

- Super-Accurate ODE Methods
- NA-NET report
- Interpolation of Multidimensional Data
- Post-Doc Position at University of Washington
- Wind Waves
- Fast Floating Point Software for Microprocessors
- Eigenvalues of Diagonally Modified Matrices
- Sabbatical Positions at Bergen Scientific Centre
- Position at Western Michigan University
- Numerical Analysis Year in Helsinki
- Happy Birthday to Van Vleck Hall

From: Nick Trefethen <lnt@math.mit.edu>

Date: Sun, 17 Apr 88 17:35:05 EDT

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: lnt@math.mit.edu OR na.trefethen@score.stanford.edu

phone: 617-253-4986

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From: Walter Gander <gander%ifi.ethz.ch@relay.cs.net>

Date: 25 Apr 88 8:37 +0100

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.

gander@ifi.ethz.ch or na.gander@na-net.stanford.edu

------------------------------

From: Peter Alfeld <MA.ALFELD@SCIENCE.UTAH.EDU>

Date: Mon 25 Apr 88 11:31:40-MDT

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,

ALFELD@SCIENCE.UTAH.EDU or NA.ALFELD@SCORE.STANFORD.EDU

------------------------------

From: Loyce Adams <adams@newton.am.washington.edu>

Date: Mon, 25 Apr 88 16:10:40 PDT

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.

------------------------------

From: Bas Bramms <BBRAAMS%PPC.MFENET@NMFECC.ARPA>

Date: Tue, 26 Apr 88 07:46:49 PDT

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;

bbraams%ppc.mfenet@nmfecc.arpa

na.braams@na-net.stanford.edu

------------------------------

From: Brad Templeton <brad%looking.uucp@relay.cs.net>

Date: Tue Apr 26 23:51:42 1988

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

that.)

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

519-884-7473.

(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

Waterloo

------------------------------

From: Hans van der Laan <RCDILAA%HDETUD1.BITNET@forsythe.stanford.edu>

Date: Wed, 27 Apr 88 16:30:50 MET

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

------------------------------

From: Pat Gaffney <FSCPG%NOBERGEN.BITNET@CUNYVM.CUNY.EDU>

Date: Wed, 27 Apr 88 14:25:32 EMT

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:

BOUNDARY ELEMENT ANALYSIS and RESERVOIR ENGINEERING

However, scientists with an interest in applying mathematics, modelling,

and numerical analysis techniques are very welcome to apply.

NA.GAFFNEY AT SCORE.STANFORD.EDU NA.REICHEL AT SCORE.STANFORD.EDU

------------------------------

From: Elise Kapenga <dedonker@anl-mcs.ARPA>

Date: Mon, 25 Apr 88 12:38:19 cdt

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

opportunities.

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 <MAT-ON%FINHUT.BITNET@forsythe.stanford.edu>

Date: Fri, 29 Apr 88 13:09:28 EET

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

Section.

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

Finland

e-mail:

RNI_MATH at FINUH.BITNET

or contact me thru na-net: na.nevanlinna

Next announcement thru na-net after summer.

Olavi Nevanlinna

------------------------------

From: Richard Brualdi <brualdi@weaver.math.wisc.edu>

Date: Thu, 28 Apr 88 12:52:31 cdt

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.

Mini-Conference

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

verify.

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

map.

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

scheduling.

5:15-5:30 Paul Terwilliger,University of Wisconsin: A

generalization of the Bose-Mesner algebra of an association

scheme.

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End of NA Digest

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