**Today's Topics:**

- A Wonderful Report
- Applied Math Is ...
- Reciprocal Pythagorean Sums
- Query About Floating Point Models
- First Annual Large Dense Linear System Survey
- Request for Domain Decomposition Bibliography
- Venice Summer School on Applied Mathematics
- Workshop for Industry in Venice
- Positions at Delft University of Tehcnology
- Positions at Australian National University
- Professur C4 fuer Mathematik in Aachen
- Contents, Linear Algebra and Its Applications

From: Gene Golub <golub@Cholesky.Stanford.EDU>

Date: Mon, 18 Mar 91 14:07:44 PST

Charlie Van Loan has written a wonderful report on recent developments

in matrix computations; it is entitled , "A Survey of Matrix

Computations." The report would make an excellent basis for a course

or seminar. If you are interested in receiving a copy, send a msg to

Charlie (na.vanloan@na-net) and ask for a copy. I'm sure you'll find

it of interest.

Gene

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

From: Joe Grcar <sepp@snll-arpagw.llnl.gov>

Date: Thu, 21 Mar 91 16:54:31 PST

I recall reading an essay titled "applied math is bad math" by

Halmos or some such, but I don't remember where. Can anyone

supply a reference? Joe Grcar, na.grcar

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

From: George Miel <MIEL@csfvax.hrl.hac.com>

Date: Mon, 18 Mar 91 19:18 PST

Reciprocal Pythagorean sums,

1/sqrt(a*a + b*b) (*)

are needed in certain applications, eg for computing Givens rotations in linear

algebraic methods. For Pythagorean sums, Moler and Morrison have presented

an algorithm that is simple, robust, and portable. Specifically, the

algorithm is attractive because it avoids range-reduction and overflow default

handling. However, the approximation of (*) based on m iterations of the

Moler-Morrison algorithm followed by reciprocation requires a total of 2m+1

divisions. For throughput intensive processors with no hardware division,

this approach is too slow. I was therefore led to the

PROBLEM: Find a division-free algorithm for reciprocal Pythagorean sums

with similar properties to the Moler-Morrison procedure, namely, with fast

convergence and no range-reduction nor overflow/underflow for a "large" set of

pairs a,b of machine numbers (say IEEE standard 754 floating point).

I have tinkered with this deceptively simple problem and so far the best I have

for single precision accuracy is an approximation for 1/sqrt(c) using a 3rd

degree polynomial approximation for the seed followed by one iteration of

Olver's method on f(x)=1/x**2-c, at a cost of 9 mult-adds. However, this

approach (as well as the usual division-free Newton-Raphson method for 1/sqrt)

requires setting c=a*a + b*b followed by range reducing c to a small interval.

Does anyone know of better alternatives?

George Miel, Hughes Research Laboratories, 3011 Malibu Cyn Rd, Malibu CA 90265

213-317-5841 miel@csfvax.hac.com

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

From: Bill White <bwhite@ucbvax.Berkeley.EDU>

Date: 15 Mar 91 17:02:00 GMT

As part of the Ada 9X effort we considering changes to the definition

of Ada floating point number representation. We are looking at two

different models: the Brown model [1] and the LCAS model [2]. We are

informally soliciting comments on the following topics.

1.) Is there any other floating point model which is likely

to be a useful candidate for the Ada 9X standard?

2.) Which of floating-point models deal best with the very

important issues of portability and robustness? In

particular, I am concerned here with the essential

difference between the non-determinism of the Brown

model and the determinism of the LCAS model.

We are inclined to favor the Brown model, in the interests of

portability. As even numerics tyros (like me) know, a major problem

with numeric computations is the whimsical nature of optimization

algorithms. It is especially problematic to tell when operands will be in

extended precision registers and when they will be dumped to memory.

The attractive aspect of the Brown model is that the non-determinism

explicitly hides the optimization effects. The more highly detemined

LCAS model requires that the numerical analyst know the optimizer's

algorithm completely. This is not always possible, or even desirable,

as the algorithms may change and improve with different compiler releases.

The particular things I am interested in are:

1.) Pointers to any other reasonable floating point models.

Since we are working in an Ada framework, the models must

be general enough to analyze IEEE floating point, but not

be restricted to a single architecture.

2.) References in the literature to analyses of numerical algorithms

which use the floating-point model explicitly. The only

one I know of is the one in Brown's original paper. I

am certain there are more, but as I am not a numerical

analyst by training I am not sure how or where to proceed.

Any help would be appreciated.

Peace,

Bill White

[1] W.S. Brown, A Simple but Realistic Model of Floating Point

Computations, ACM Transactions on Mathematical Software, vol 7,

(1981) pp. 445-480.

[2] Mary Payne, Craig Schaffert, and Brian Wichmann, Proposal for a

Language Compatible Arithmetic Standard, appeared in SIGPLAN

Notices, vol 25, no 1., January 1991, pp. 59-86.

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

From: Alan Edelman <edelman@math.berkeley.edu>

Date: Sat, 23 Mar 91 23:27:24 PST

THE FIRST ANNUAL LARGE DENSE LINEAR SYSTEM SURVEY

Without realizing it, about a year ago, I initiated the 0th annual large

dense linear system survey here in NANET. I've had so many requests

for a repeat survey that I decided to formalize the process by making it a

yearly event. (My calendar file should remind me to repeat this next year.)

I understand the NANET list has grown considerably since last time, so this

survey should reach many more people.

By default, none of the information you supply will be anonymous, however

I will keep any information strictly confidential upon request.

All of these questions relate to large DENSE linear systems.

Feel free to interject any comments between the lines, etc.

Results will be tallied into a LaTeX paper and will be available by

anonymous FTP from math.berkeley.edu.

Name __________________

Address _______________

_______________

_______________

_______________

Type of Institution ___ University ___ Independent Research Lab

___ Aircraft industry ___ Supercomputer Manufacturer

___ Other

Largest matrix size that you solved n=_________

Length of time ___________ (seconds, hours, weeks, ...)

on which machine ________________

Matrix was generated from ___ Moment Methods

___ Panel Methods for Lifting Potential Flow

___ Panel Methods for Potential Flow

___ Randomly (specify the distribution)

___ Other

Solution method used was ____ LU factorization

____ An iterative Method (Please specify___________)

(If an iterative method was used, did you take advantage of

symmetry, diagonal dominance, or any property at all?)

The solver was ___ your own

___ from a package (Please specify___________________)

The accuracy of the solution obtained

____ was clearly good (Specify how you know ____________________)

____ seems okay, but you are not really sure

____ is unknown

Any other comments, suggested questions for next year, etc?

I'm aware that aircraft manufacturers and supercomputing companies would be

most interested in these results, but might be reluctant to reveal their own

secrets. I would like to urge such manufacturers to feel free to mail me

anonymous responses by surface mail even without return addresses and names.

I will guarantee anonymity in any case upon request. Everyone will so benefit.

All I ask is that responses be truthful.

I trust that the academics out there who are doing this will be more than

happy to be forthcoming.

edelman@math.berkeley.edu

Alan Edelman

Dept of Mathematics

University of California

Berkeley, CA 94720

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

From: Jeff Scroggs <scroggs@matjfs.ncsu.edu>

Date: Sat, 23 Mar 91 17:00:16 -0500

Louise Perkins and Jeff Scroggs would like to request bibliographic

data on heterogeneous domain decomposition. We are interested

in papers that deal with domain decomposition techniques for the

numerical solution of PDEs in which different modeling equations are

used in different subdomains.

This data will be collected into a publicly available report (issued

by ICASE, NASA Langley Research Center).

In order that this database be manageable, we have the following request:

Format: Bibliographic data should be in bibtex format. A set of

keywords is requested as part of the format.

Medium: Email messages to Louise Perkins or Jeff Scroggs.

Date: References for the first version should be in by April 5.

Assistance: To assist with placing the data in bibtex

format, send a request to either of us for the C

program BIBINPUT. This program will interactively

prompt you for the data, and produce a file with the

formatted entries.

Disclaimer: We are trying to keep this bibliography focused, hence

submissions that do not obviously deal with heterogeneous

domain decomposition will be eliminated.

Louise Perkins

54-1420

MIT

Cambridge, MA 02139

(617)253-1291

perkins@pimms.mit.edu

Jeffrey S. Scroggs

Box 8205

Mathematics Department

North Carolina State University

(919)737-7817

scroggs@matjfs.ncsu.edu

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

From: Renato Spigler <SPIGLER%IPDUNIV@ICNUCEVM.CNUCE.CNR.IT>

Date: Tue, 19 Mar 91 14:17:19 SET

Between June 17 and 28, 1991, a Summer School will be held in Venice, Italy,

downtown, at the Ateneo Veneto (Campo S.Fantin 1897,S.Marco,30124 Venice).

Speakers and topics will be

1) G.H.GOLUB, Stanford, "Matrices,moments,and orthogonal polynomials",

2) E.HAMEIRI, Courant Institute, NYU, "Localized instabilities in MHD plasmas

and in classical fluids",

3) P.A.MARKOWICH, TU-Berlin and Purdue, "Mathematical modelling of

semiconductors",

4) G.MILTON, Courant Institute, NYU, "Exploring the properties of composite

materials".

The Scientific Committee includes V.Boffi, F.Brezzi, G.Frosali, and D.Trigiante.

Attendence will be limited to 50 participants. Send applications to Renato

SPIGLER, Dipartimento di Metodi Mod. Mat. Sci. Appl., Universita' di Padova,

Via Belzoni, 7-35131 Padova (Italy), phone 0039-49-83 19 14, 83 19 01 ,

fax 0039-49-83 19 95, e-mail spigler at ipduniv.bitnet.

The event is sponsored/jointly organized/with the collaboration of

Universita' di Padova

Gruppo Nazionale per la Fisica Matematica del CNR

UNESCO

Courant Institute of Mathematical Sciences, NYU

SIAM

Renato Spigler

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

From: Renato Spigler <SPIGLER%IPDUNIV@ICNUCEVM.CNUCE.CNR.IT>

Date: Tue, 19 Mar 91 14:52:44 SET

On May 3, 1991, there will be a one-day workshop on Mathematics for Industry,

in Venice, Italy, at the Istituto Veneto di Scienze, Lettere e Arti

(Campo S.Stefano, S.Marco 2945). This event is promoted by ALPE ADRIA,

the J. Kepler University of Linz, S.A.S.I.A.M.-Tecnopolis, and the

University of Padova. It will also held under the auspices of the European

Consortium for mathematics in the Industry (ECMI), and the Consorzio

Venezia-Ricerche.

Four mathematicians from the Academia and two or three from the industrial

worldwill present a few case studies, as examples of successful collaboration

between the two environments. A free, informal discussion willbe organized in

the afternoon, and, possibly, some new, open problems will be introduced for

the purpose of establishing new collaborations.

The event is aimed mainly to the Alpe Adria community.

Renato Spigler

(phone 0039-49-831914, 831901, fax 831995, e-mail spigler at ipduniv.bitnet)

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

From: Ed F. Deprettere <ed@dutentb.ET.TUDelft.NL>

Date: Tue, 19 Mar 91 17:51:00 +0100

Faculty and PH.D candidate positions available, Network Theory Section

(Microelectronics Group), Department of Electrical Engineering,

Delft University of Technology, Delft The Netherlands.

Junior Scientist Position

and

Ph.D. Candidate Position

In connection with the project Modeling and Determination of

Parasitics in Submicron VLSI Layouts at the Network Theory

Section of the Faculty of Electrical Engineering at Delft

University of Technology, Delft, The Netherlands, the above

mentioned positions are currently open.

The project aims at an advanced system for the modeling of

submicron IC interconnect structures. The ongoing

miniaturization of IC's-0.5 micron feature size is quickly

becoming available-causes new design related problems.

Because of their minute dimensions, the circuit elements

behave differently. One aspect of this changed behavior is

the relative increase of parasitic resistances, ground

capacitances and coupling capacitances. An IC designer who

does not properly account for these effects runs the risk

that his design does not function as intended. The problem

is especially severe in combined analog/digital (e.g.

BICMOS) circuits.

Not only are these parasitic effects becoming more

prominent, they are also becoming more difficult to

determine: traditional, heuristic methods are inadequate.

Instead, completely new methods are necessary to capture

these effects into suitable models. The goal of the present

case project is to develop these methods and models.

TASK

You will be part of a team carrying out research to develop

such a modeling system. You will build on the knowledge

available in the laboratory, as was developed in a precursor

project. After a thorough study of those results, you will

extend the theory in order to come to a system capable of

delivering accurate (but not over-accurate) models that

enable designers to predict the crosstalk between different

subcircuits. Relevant physical aspects are e.g.:

+ interconnect capacitances of non-planar structures,

+ capacitive effects of diffused conductors,

+ the resistive nature of the substrate.

The newly developed theory will lead towards a prototype

implementation in the Nelsis IC design system.

REQUIREMENTS

The positions can be characterized as multi-disciplinary:

electrical engineering, physics, linear algebra, numerical

mathematics and computer science are all relevant.

Applicants should have a grade in one of these disciplines,

preferably their education and/or experience shows a good

mix of these disciplines. It is the intention that the

research will lead to dissertations.

NOTE

An appointment will be temporal with a duration of 4 years.

INFORMATION

For more information, please apply to

Dr. N.P. van der Meijs

tel. +31-15-786258

email: nick@et.tudelft.nl

or

Prof. P. Dewilde

tel. +31-15-786234,

email: dewilde@dutentb.et.tudelft.nl.

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

From: Mike Osborne <mike@thrain.anu.edu.au.

Date: Wed, 20 Mar 91 07:37:32 +1000

The Australian National University

Centre for Information Science Research

ANU Supercomputer Facility

Research Positions

Advanced Computational Mathematics Software Development

The ANU and Fujitsu Japan have established a large number of research

and development projects in advanced computing and its applications

under the general direction of the Centre for Information Science

Research at the University. This Centre, established as part of a

strategic plan by the University to create a centre of international

standing, acts as a focus of advanced computing throughout the

University and brings together diverse groups in the Institute of

Advanced Studies and The Faculties involved in advanced computing

research and teaching.

The ANU has assembled one of the most powerful and broadly-based

advanced computing environments to be found in a university. Advanced

computing resources at the ANU include a Fujitsu VP2000 vector

processor, a Connection Machine with 16K processors and a 128

processor Fujitsu AP1000. Each machine is capable of peak speeds of

over 1 Gigaflops.

Two positions are now available in a new project to develop

state-of-the-art mathematical software for a parallel vector

processing environment. Mathematicians with experience in algorithm

and software development are sought to join this project which is

under the direction of staff from the School of Mathematical Sciences

and the Computer Science Laboratory, Research School of Physical

Sciences and Engineering. Appointees will be expected to interact

closely with these groups which are also engaged in the development of

algorithms and software for the experimental multi-processor AP1000

supercomputer.

These positions are centred on algorithm and software development for

the parallel models of the VP2000 series of vector processors.

Appointees will be required to work on software development for

eigenvalue problems or Fast Fourier Transforms. Access to a

multi-processor VP2000 series machine will be made available.

Applicants should have a firm background in computational mathematics

and a higher degree in a scientific or mathematical discipline with

considerable research experience. Less experienced and qualified

candidates may also be considered. We are particularly seeking

computational mathematicians with an interest in eigenvalue problems

and FFTs. Experience or a deep understanding of parallel or vector

processing or experience in software development would be very

advantageous. The ability to complete projects on schedule is

essential.

The duration of the appointment will be initially for one year, but it

is hoped that funding will become available over a longer period.

Persons wishing to take the posts on secondment from other positions

are encouraged to apply. Appropriate financial arrangements will be

made with the appointee's home institution in this case.

Other appointments will be normally made to an academic position in

the range of Post-doctoral Fellow ($28792-$32762) through to Senior

Research Fellow ($45729-$54255). The level of appointment will

reflect the candidate's experience.

Further information is available from, Dr R Gingold, Phone: (06) 249

3437 or 249 4519. Fax: 247 3425. E-mail: rag900@anusf.anu.edu.au.or

Professor R Brent (249 3329) or Professor M Osborne (249 4501).

Applications including curriculum vitae, list of publications and the

names and addresses (including Fax) of three referees should be

submitted in duplicate to The Registrar, The Australian National

University, GPO Box 4, Canberra ACT Australia 2601 by the closing date

April 15. Post no. CISR 13.3.1

The University reserves the right not to make an appointment

or to appoint by invitation at any time. The ANU is an equal

opportunity employer.

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

From: Karl-Heinz Brakhage <EZ010BR%DACTH11.BITNET>

Date: Wed, 20 Mar 91 17:50:10 MEZ

RHEINISCH-WESTFAELISCHE TECHNISCHE HOCHSCHULE AACHEN

In der Mathematisch-Naturwissenschaftlichen Fakultaet ist am Institut

fuer Geometrie und Praktische Mathematik eine

P R O F E S S U R C 4 F U E R M A T H E M A T I K

(Fiebiger-Programm)

zu besetzen.

Erwartet wird die Vetretung des Faches Mathematik in Forschung und

Lehre und die Mitwirkung an der Ausbildung von Studierenden der

Mathematik, Ingenieur- und Naturwissenschaften. Zu den Aufgaben des

Institutes gehoert das Vorlesungsangebot in Numerik sowie

Darstellender Geometrie.

Erwuenscht ist ein Forschungsgebiet aus der Numerischen Analysis, das

Bezug zu Ingenieur- und Naturwissenschaften hat, z.B. Numerische

Mathematik der Differentialgleichungen oder/und numerisch-geometrische

Verfahren fuer hoeher dimensionale Probleme.

Einstellungsvoraussetzung sind Habilitation oder gleichwertige

wissenschaftliche Leistungen sowie paedagogische Eignung.

Die Bewerbung von Schwerbehinderten ist erwuenscht.

Bewerberinnen und Bewerber werden gebeten, sich mit den ueblichen

Unterlagen (Lebenslauf, Darstellung des wissenschaftlichen bzw.

beruflichen Werdegangs, Schriftenverzeichnis) bis zum

15. Mai 1991

an den

Dekan der Mathematisch-Naturwissenschaftlichen

Fakultaet der RWTH Aachen

Templergraben 64

D-5100 Aachen.

Auch Hinweise auf geeignete Persoenlichkeiten sind erwuenscht.

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

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

Date: Wed, 20 Mar 91 10:25:48 cst

Table of Contents of Volume 150 of LAA, May 1991:

Proceedings of the First Conference of the International

Linear Algebra Society

Special Editors: Wayne Barrett, Daniel Hershkowitz,

and Donald Robinson

George W. Soules (Princeton, New Jersey)

The Rate of Convergence of Sinkhorn Balancing 3

Marvin Marcus (Santa Barbara, California)

Multilinear Methods in Linear Algebra 41

Russell Merris (Hayward, California)

Almost All Trees Are Co-immanantal 61

Daniel J. Scully (Saint Cloud, Minnesota)

Maximal Rank-One Spaces of Matrices Over Chain Semirings. I. u-Spaces 67

Ronald J. Stern (Montreal, Quebec, Canada) and

Henry Wolkowicz (Waterloo, Ontario, Canada)

Invariant Ellipsoidal Cones 81

Bob Grone and Steve Pierce (San Diego, California)

Extremal Positive Semidefinite Doubly Stochastic Matrices 107

Shmuel Friedland (Chicago, Illinois)

Pairs of Matrices Which Do Not Admit A Complementary Triangular Form 119

Jerome Dancis (College, Park, Maryland)

Invertible Completions of Band Matrices 125

R. Loewy, D. R. Shier, and C. R. Johnson

(Williamsburg, Virginia)

Perron Eigenvectors and the Symmetric Transportation

Polytope 139

I. Gohberg (Ramat Aviv, Israel), M. A. Kaashoek

(Amsterdam, The Netherlands), and H. J. Woerdeman

(La Jolla, California)

A Note on Extensions of Band Matrices With Maximal and

Submaximal Invertible Blocks 157

Robert Grone (San Diego, California)

On the Geometry and Laplacian of a Graph 167

Chi-Kwong Li (Williamsburg, Virginia) and Nam-Kiu Tsing

(College Park, Maryland)

G-Invariant Norms and G(c)-Radii 179

Michael E. Lundquist (Provo, Utah) and

Charles R. Johnson (Williamsburg, Virginia)

Linearly Constrained Positive Definite Completions 195

Rafael Bru (Valencia, Spain), Leiba Rodman

(Williamsburg, Virginia), and Hans Schneider

(Madison, Wisconsin)

Extensions of Jordan Bases for Invariant Subspaces of a Matrix 209

R. A. Brualdi (Madison, Wisconsin) and

J. Csima (Hamilton, Ontario, Canada)

Small Matrices of Large Dimension 227

Yik-Hoi Au-Yeung and Che-Man Cheng (Hong Kong)

Permutation Matrices Whose Convex Combinations

Are Orthostochastic 243

Jeffrey L. Stuart (Hattiesburg, Mississippi) and

James R. Weaver (Pensacola, Florida)

Matrices That Commute With a Permutation Matrix 255

Jean H. Bevis and Frank J. Hall (Atlanta, Georgia)

Integer LU-Factorizations 267

Pal Rozsa (Budapest, Hungary), Roberto Bevilacqua,

Francesco Romani, and Paola Favati (Pisa, Italy)

On Band Matrices and Their Inverses 287

Charles R. Johnson (Williamsburg, Virginia) and

Erik A. Schreiner (Kalamazoo, Michigan)

Explicit Jordan Form for Certain Block Triangular Matrices 297

Jorma Kaarlo Merikoski (Tampere, Finland)

On c-Norms and c-Antinorms on Cones 315

R. B. Bapat (New Delhi, India)

An Interlacing Theorem for Tridiagonal Matrices 331

Olga Taussky and John Todd (Pasadena, California)

Another Look at a Matrix of Mark Kac 341

M. C. Gouveia (Coimbra, Portugal) and R. Puystjens

(Gent, Belgie@a2)

About the Group Inverse and Moore-Penrose Inverse of a Product 361

Hans Joachim Werner (Bonn, Germany)

Some Further Results on Matrix Monotonicity 371

Yair Censor (Haifa, Israel) and Stavros A. Zenios

(Philadelphia, Pennsylvania)

Interval-Constrained Matrix Balancing 393

Shmuel Friedland (Chicago, Illinois)

Quadratic Forms and the Graph Isomorphism Problem 423

H. Bart (Rotterdam, The Netherlands) and H. K. Wimmer

(Wurzburg, Germany)

Simultaneous Reduction to Triangular and Companion Forms

of Pairs of Matrices: The Case rank(I_AZ)=1 443

Wayne Barrett, Donald Robinson (Provo, Utah),

and Daniel Hershkowitz (Haifa, Israel)

REPORT: Inaugural Conference of the International Linear Algebra Society, 12-15 August 1989, Brigham Young University, Provo, Utah, USA 463

Special Issues in Progress

1. Interior Point Methods for Linear Programming; special editors are D. Gay, M.

Kojima, and R. Tapia. To appear as Volume 152, July 1, 1991.

2. Iterations in Linear Algebra and Its Applications (Dedicated to G. H. Golub,

R. S. Varga, and D. M. Young); special editors are O. Axelsson, J. de Pillis,

M. Neumann, W. Niethammer, and R. J. Plemmons. To appear as Volumes 154/155,

August/September 199

3. Algebraic Linear Algebra; special editors are Robert M. Guralnick, William H.

Gustafson, and Lawrence S. Levy. To appear as Volume 157, October 15, 1991.

4. Proceedings of the Auburn 1990 Matrix Theory Conference; special editors are

David Carlson and Frank Uhlig. Submission deadline: August 1, 1990. Details

provided with the conference announcement.

5. Proceedings of the Sixth Haifa Conference on Matrix Theory; special editors

are A. Berman, M. Goldberg, and D. Hershkowitz. Submission deadline: October 1,

1990. Details provided with the conference announcement.

6. Proceedings of the International Workshop on Linear Models, Experimental

Designs and Related Matrix Theory, (August 6-8, 1990, Tampere, Finland);

special editors are Jerzy K. Baksalary and George Styan. Submission deadline:

October 31, 1990. Details provided with the conference announcement.

7. Proceedings of the Second NIU Conference on Linear Algebra, Numerical Linear

Algebra and Applications, (May 3-5, 1991, Northern Illinois University, DeKalb,

Illinois); special editors are Biswa Dutta and Robert Plemmons. Submission

deadline: July 31, 1991. Details provided with the conference announcement.

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

End of NA Digest

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