NA Digest Sunday, April 24, 1988 Volume 88 : Issue 17

Today's Editor: Cleve Moler

Today's Topics:


From: Julius Smith <Julius_Smith@NeXT.COM>
Date: Tue, 19 Apr 88 12:08:52 PDT
Subject: Factoring an Inverse Toeplitz Matrix


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
Subject: Appeal for Spase Matrix Test Problems

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
Subject: Research Associate Positions at RIACS

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.


Date: Fri, 22 Apr 88 10:23:09 EMT
Subject: More on the Tromsoe, Norway, Conference


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


From: Spiros Tsaltas <ncar!noao!amethyst!tsaltas@AMES.ARC.NASA.GOV>
Date: 22 Apr 88 07:47:40 GMT
Subject: "Boundary Element Research" for Sale

For sale :

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

Thanks for your attention,
Dept. of Math., Univ. of Arizona


From: Tom Coleman <>
Date: Sun, 24 Apr 88 10:31:32 EDT
Subject: Postdoc Position at Cornell

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
Tom Coleman, Computer Science Department, Upson Hall,Cornell University,
Ithaca NY 14853.

End of NA Digest


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Subject: addendum to v88.17
Status: R

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

<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: OR
phone: 617-253-4986