**Today's Topics:**

- Code Requested for Matrix Factorizations
- Public Domain QP solvers Needed
- Rational Approximation Info Wanted
- Object-Oriented Programming for Numerical Applications
- Generating Eigenvalues in a Particular Order
- Change of Address for Stavros A. Zenios
- Conference on Hyperbolic Problems
- IMSL User Group Conferences

From: John Conroy <super!conroy@uunet.uu.net>

Date: 28 Dec 89 21:56:09 GMT

Does anyone have code (Fortran or C) to compute:

1. the C-S decompostion of an orthogonal matrix

2. the solution of a hermitian, positive definite Toeplitz system.

I checked netlib and the best I found for 2 is a program to solve

the general complex Toeplitz case. In addition, I could not

find any entries in netlib to perform the C-S decomposition.

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

From: Arvind Srinivasan <sarvind@somewhere.Berkeley.EDU>

Date: 31 Dec 89 00:38:16 GMT

Does anyone know of public domain Quadratic Programming

packages which are available through anonymous ftp

or for a nominal fee? I am interested in solving

large-scale sparse problems.

Thanks for any info,

Arvind Srinivasan.

University of California, Berkeley

e-mail: sarvind@somewhere.Berkeley.EDU

BITNET: sarvind@ucbjanus.BITNET

Phone : 1+415-642-4325

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

Date: 1 Jan 90 22:37:20 GMT

From: Wm Randolph Franklin <wrf@cs.rpi.edu>

I am interested in approximating a smooth function with these

properties.

- The function has at most 2 extrema in the interval of interest.

- It is differentiable several times.

- It is an actual function, although w/o an explicit representation.

- The function involves inverting a parametric function, and

substituting into another explicit function.

- I want to interpolate it at 1000 equally spaced points, and

- need the answers to only 0.001 accuracy or worse.

- The function may have complex poles near the interval.

- The application, FYI, involves functions of normals to parametric

bicubic surfaces.

I would like to find a rational approximation to the function.

I would really like is a cookbook for rational approximations

saying how to find them and when they are valid. Is there any such

thing? If not, are there recent papers at least?

Thanks.

Wm. Randolph Franklin

Rensselaer Polytechnic Institute, Troy NY

Internet: wrf@ecse.rpi.edu (or @cs.rpi.edu) Bitnet: Wrfrankl@Rpitsmts

Telephone: (518) 276-6077; Telex: 6716050 RPI TROU; Fax: (518) 276-6261

Paper: ECSE Dept., 6026 JEC, Rensselaer Polytechnic Inst, Troy NY, 12180

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

From: Brian Smith <smith@knuth.cs.unm.edu>

Date: Thu, 4 Jan 90 13:57:51 -0700

George Luger from our UNM CS department asked me if I knew of any papers on

the use of object-oriented programming techniques applied to numerical

software. I cannot recall any but I thought that possibly a request over

na-net for George might provide him with the information.

Do you know of papers or technical reports describing the use of

object-oriented programming techniques in numerical applications?

Please send responses to luger@unmvax.cs.unm.edu

Thanks.

Brian Smith

CS Dept.

Univ. of New Mexico

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

From: Farid Alizadeh <alizadeh@UMN-CS.CS.UMN.EDU>

Date: 6 Jan 90 04:28:37 GMT

A few months ago I posted a question in na.net regarding the generation of

eigenvalues of a real, symmetric matrix with some of the entries variables, in

such a way that the eigenvalues generated are smooth functions of variable

entries in the matrix. I received numerous responses and a couple of papers.

But none of them answered the problem satisfactorily.

Here is where the problem actually arose:

Let A(x) be a real symmetric mxm matrix and vector x the list of variables

in the matrix. Consider the following optimization problem:

minimize f(x) + z

subject to

l_i(x) - z >0 for i=1,...,m

where x is in R^n, l_i(x) is the i'th eigenvalue of A(x), z is a variable and

f(x) is some function which is at least doubly differentiable. Suppose now

we want to use any of the well-known methods such as Lagrangian methods or

gradient projection method to solve this problem. The trouble is that the

success of such methods depends on differentiability of constraints, in this

case functions l_i(x). Now, we know how to generate eigenvalues, but we do not

know how to reorder them so that from a point x_k to a point x_k+1 the function

l_i varies smoothly. Thus we need to reorder the eigenvalues generated so

that each l_i corresponds to a smooth function.

I still do not know how to generate the eigenvalues smoothly, however in this

particular problem I sidestep the trouble by two different methods.

The first method is to forget about Lagrangian or gradient projection

algorithms and resort to barrier methood. In that case the order will be

unimportant because the barrier function

f(x) + z - r*[(l_1(x) - z )^(-1) + ... + (l_n(x) - z)^(-1)]

(or any other barrier function) lumps the constraints together and makes

their order irrelevant. (Penalty methods will also work for the same reason.)

However, barrier methods are known to be slow and

result in ill-conditioned problems near the solution. This brings us to

another alternative, that is, to replaceing the constraints by an equivalent set

of constraints. Note that the constraints l_i(x) - z > 0 for i=1,...,m

are equivalent to saying that the matrix A(x) - z*I is positive semi-definite

and therefore, its leading principal minors are non-negative. So, I replace

the original problem with:

minimize f(x) + z

s.t.

det_i [A(x) - z*I] > 0 for i=1,...,m

where det_i(A) is the determinant of the leading ixi principal submatrix of A.

In this problem the constraints and their derivatives are easily

computable. So we may use any of the well-known optimization techniques.

I hope this will be of some use to people who requested for responses to

the problem I had posted. I would appreciate any other ideas, and I still

would like to know how to rearrange eigenvalues so that the i'th element in the

list varies smoothly as the variables in the matrix A(x) change.

Farid Alizadeh

Computer Science Dept.

University of Minnesota

Mineapolis, Mn, 55455

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

From: Stavros A. Zenios <ZENIOS@wharton.upenn.edu>

Date: Sat, 6 Jan 90 13:01 EDT

For the period January 1 - August 31, 1990 I will be

visiting the OR Center at the Sloan School, MIT

and Thinking Machines Corporation. Please note the change of

address:

Stavros A. Zenios

Thinking Machines Corporation

245 First Street

Cambridge, MA 02142--1214

Telephone nos.

MIT: (617) 253--3622

TMC: (617) 876--1111, ext. 2448

e-mail:

Mail sent trough NAnet or directly to

zenios@wharton.upenn.edu will reach me.

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

From: Bertil Gustafsson <BERTIL@TDB>

Date: Thu, 28 Dec 89 15:04 MET

THIRD INTERNATIONAL CONFERENCE ON HYPERBOLIC PROBLEMS

UPPSALA, SWEDEN

June 11-15, 1990

Second announcement and call for papers

The objective of the conference is to bring together researchers with interest

in the theoretical, applied and computational aspects of hyperbolic partial

differential equations. Theory of hyperbolic partial differential equations and

in particular nonlinear problems will be discussed. Analysis and applications

of numerical methods will be an important part of the conference. Application

to different fields such as aerodynamics, meteorology, oceanography, elastic

and electromagnetic wave propagation and combustion will be considered.

This is the third in a series of conferences on hyperbolic problems. The first

was held in St. Etienne, France in 1986, the second in Aachen, Federal Republic

of Germany in 1988 and the fourth will take place in Italy 1992.

Professor Heinz-Otto Kreiss will be 60 years old during 1990. The significance

of his contributions to all research areas in hyperbolic problems is well

known. In 1965 he became the first professor in Numerical Analysis at Uppsala

University; this was the first chair in the newly formed Department of

Scientific Computing. It is therefore natural to dedicate this conference to

Professor Kreiss.

ORGANISATION: Department of Scientific Computing, Uppsala University

ORGANIZING COMMITTEE: Bjorn Engquist, Bertil Gustafsson

CONFERENCE SECRETARY: Lena Jutestahl

REGISTRATION: The registration fee 900 SEK can be paid by check issued to

"Department of Scientific Cmputing". The fee is 1200 SEK if paid after May 1,

1990.

CALL FOR PAPERS: Abstracts for presentations at the conference are invited. The

abstract should be at least one full page and at most three pages. The

presentation is expected to be 20 minutes. The deadline for the abstracts is

February 1, 1990. Notification of acceptance will be given by March 31. Copies

of all accepted abstracts will be distributed at the conference.

PROCEEDINGS: Conference proceedings will be published. Instructions for the

form of the submitted papers will be sent to the speakers. The papers are due

August 31, 1990.

LOCATION: The conference will be held in the Main University Building in the

center of Uppsala. The city is located 70 km:s north of Stockholm with easy

access to the Stockholm Airport. Uppsala has old historical traditions dating

back to the Viking time. The university was founded 1477 and is among the

oldest in Europe.

ACCOMODATION: A block of hotel rooms has been reserved at discount prices for

the conference participants. The price range is 500-800 SEK per day in single

room. Double rooms are also available.

If you want to ___ attend the conference

___ present a paper

___ reserve a hotel room

please write to

Lena Jutestahl

Dept of Scientific Computing

Uppsala University

Sturegatan 4B

S-75223 Uppsala

Sweden

Fax: 018-123049; Int: +46 18123049

E-mail: "LENA at TDB.UU.SE"

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

From: Tracy Seguin <imsl!seguin@uunet.uu.net>

Date: 5 Jan 90 18:30:55 GMT

IMSL USER GROUP/NORTH AMERICA CONFERENCE

May 9-11, 1990

Monterey, California

IMSL USER GROUP/EUROPE CONFERENCE

March 26-28, 1990

Bologna, Italy

The theme of this year's conferences is "Applications

of Mathematical/Statistical Libraries and Problem-Solving

Systems".

The IMSL User Group Europe is a not-for-profit organization,

offering a forum where professionals can exchange ideas on

applications and methodologies of mathematical and statistical

software. The user group is composed of a diverse group of

professionals, such as data center managers, technical support

analysts, programmers, software developers, scientists,

engineers, and educators, all with a common interest in the

evolution, development, and practical application of mathematical

and statistical software.

A new feature at this year's conference will be a series of

tutorials covering topics concerning IMSL product installation,

advanced applications, and services. IMSL will provide these

tutorials at no charge to attendees of the conference. Take

advantage of this unique opportunity to expand your knowledge of

IMSL software and increase your personal productivity.

To submit a paper or for further information on attending a

conference, please contact:

IMSL User Group North America

Dennis Mar

Naval Post Graduate School

1332 Lincoln Avenue

Pacific Grove, CA 93950

e-mail:uunet!navpgs.bitnet!2001p

telephone: (408) 646-2672

IMSL User Group Europe

Dr. Marco Vaccari

ENEA

Department TIB/CALC/DATINU

Viale Ercolani, 8

I-40138 Bologna

Italy

email uunet!iboenea.bitnet!birac1

tel 39 51 498314/498173/498111

facsimile 39 51 498359/498151

telex 511578 ENEABO I

IMSL User Group Liaison

Laurie Potratz

P.O. Box 4605

Houston, Texas 77210-4605

e-mail: uunet!imsl!lpotratz

telephone: (713) 782-6060

facsimile: (713) 782-6069

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

End of NA Digest

**************************

-------