**Today's Topics:**

- Factoring an Inverse Toeplitz Matrix
- Appeal for Spase Matrix Test Problems
- Research Associate Positions at RIACS
- More on the Tromsoe, Norway, Conference
- "Boundary Element Research" for Sale
- Postdoc Position at Cornell

From: Julius Smith <Julius_Smith@NeXT.COM>

Date: Tue, 19 Apr 88 12:08:52 PDT

Greetings,

As I recall, someone from NA land inquired about software

for computing the Cholesky factor of the inverse of a

symmetric Toeplitz matrix. I have recently written a

Fortran subroutine to do this. It uses the Levinson recursion

described in Benjamin Friedlander, "Lattice Filters for Adaptive

Processing", Proc. IEEE, vol. 70, pp. 829-867, Aug. 1982.

I will be glad to e-mail my routine to anybody requesting it.

It's short -- less than 200 lines including a test driver.

-- Julius Smith

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

From: Iain Duff <duff@anl-mcs.ARPA>

Date: Thu, 21 Apr 88 02:40:38 cst

As many of you know we (i.e. Harwell), together with Boeing, maintain and

distribute a set of sparse matrix test problems. It now transpires that

I need more problems in two areas in which the present set is somewhat

deficient. I would appreciate problems (preferably in the Harwell-Boeing

format ... sent on request) in two areas.

1. Sparse least-squares problems ... together with right-hand side(s).

These should be large but not necessarily huge (i.e. thousands or

tens of thousands of rows rather than millions).

2. Unassembled problems from finite element applications. Preferably but

not necessarily with real values.

I intend to use these problems to test current algorithms and approaches

currently being undertaken at Harwell and will assuredly give adequate

reference to the source of any problem used. Any really interesting

cases may (with the consent of the originator) be incorporated in a future

release of the main Harwell-Boeing test set.

Iain Duff

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

From: Rich Sincovec <sincovec@boulder.Colorado.EDU>

Date: Fri, 22 Apr 88 10:49:08 MDT

Several research associate positions are available at RIACS (Research

Institute for Advanced Computer Science). These positions involve

collaboration with senior scientists in exploring and implementing

algorithms for highly parallel architectures (including 16,000 processor

CM-2). Excellent salary and benefits. Masters in Computer Science or

Applied Math desirable. Send resume to Center for Advanced Architectures,

Research Institute for Advanced Computer Science, Mail Stop 230-5,

Moffett Field, CA 94035. Equal Opportunity Employer. Must be U.S.

citizen or permanent resident.

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

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

Date: Fri, 22 Apr 88 10:23:09 EMT

DEADLINE FOR TROMSOE CONFERENCE REGISTRATION

The registration fee for the Tromsoe conference is NOK 2200 before April 29.

AFTER APRIL 29 the registration fee is NOK 3500.

For those of you who do not feel that the conference provides enough social

events we have obtained the following offer:

On Saturday evening June 4 at midnight there will be an excursion to Svalbard

(a group of islands north of Norway)

The excursion leaves by plane at Midnight from Tromsoe, there is a guided tour

by plane, landing on longyearbyen for a light meal, then return to Tromsoe

at 6am on Sunday morning.

The cost is NOK 1800 per person.

For those of you who feel like starting the week well, the excursion can also

be arranged starting on Sunday night and returning Monday morning, 2 hours

before the conference starts|

If you are interested in either of these then please contact me directly

telling which day you are interested in. Because of the size of the plane

the excursion is limited to 100 people. Therefore, first come first served|

Pat Gaffney

NA.GAFFNEY AT NA-NET.STANFORD.EDU

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

From: Spiros Tsaltas <ncar!noao!amethyst!tsaltas@AMES.ARC.NASA.GOV>

Date: 22 Apr 88 07:47:40 GMT

For sale :

BOUNDARY ELEMENT RESEARCH (edited ) by C.A.Brebbia

ISNB 0-931215-02-1 CML Publications 1985.

Original price: 23 British Pounds, very slightly used.

Price: make me an offer at tsaltas@arizrvax.bitnet

or tsaltas@amethyst.ma.arizona.edu

Thanks for your attention,

Spiros.

Dept. of Math., Univ. of Arizona

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

From: Tom Coleman <coleman@gvax.cs.cornell.edu>

Date: Sun, 24 Apr 88 10:31:32 EDT

The Cornell Computational Optimization Project (Bland, Coleman,

Todd, Trotter, Van Loan) has money to support a postdoc for the next

1-2 years. Start date is somewhat flexible and the main requirement

is a serious interest in computational optimization. The only

duty is: Research !

Besides the listed faculty, we have a number of students and another

optimization postdoc (Yuying Li from Waterloo, supported by the Mathematical

Sciences Institute) interested in computational optimization. Equipment:

there is a (10) Sun-lab devoted to CCOP activities and a new 32-node Intel/2

hypercube. Also accessible are various high performance computers

housed by the Theory Center.

Please spread the word to graduating students etc. and ask them to

contact me if interested. Thanks.

Tom Coleman

coleman@gvax.cs.cornell.edu

or

607-255-9203

or

Tom Coleman, Computer Science Department, Upson Hall,Cornell University,

Ithaca NY 14853.

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

End of NA Digest

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From: nanet@Patience.stanford.edu (The NA-NET)

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To: na@na-net.stanford.edu

Subject: addendum to v88.17

Status: R

>From lnt@math.mit.edu Sun, 17 Apr 88 17:35:05 EDT

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

Subject: Super-Accurate ODE Methods

To: na@na-net.stanford.edu

<This was overlooked for digest v88.17. -mark>

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