### Today's Editor:

- Cleve Moler
- The MathWorks, Inc.
- moler@mathworks.com

- Lawson & Hanson Least Squares Code
- Re: Did Roundoff Cause Patriot Failure?
- Who was Raphson? (an answer)
- Overlaying Postscript Figures with LaTeX Fragments
- SISSC Table of Contents Online
- New Book by Bryne and Schiesser
- Two New Books
- CERFACS Annual Report by FTP
- CTAC93 Meeting in Australia
- Parallel Numerical Analysis Workshop `92: PROGRAM
- Positions at University of Bergen
- Linear Algebra and its Applications

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

From: Chuck Lawson <clawson@math.Jpl.Nasa.Gov>

Date: Tue, 2 Jun 92 12:01:53 PDT

**Subject: Lawson & Hanson Least Squares Code**

Answering the query by Ferguson in the NA Digest re

a source for the code from the Lawson & Hanson book,

Solving Least Squares Problems.

This code was available from IMSL from the publication

of the book (1974) up to a couple of years ago. At that

time IMSL decided to quit handling distribution of

ACM TOMS algorithms and miscellaneous software packages.

C. Abaci, Inc., (Phone 919-832-4847) has taken on much of

this distribution service. In particular the

Lawson & Hanson code, called LLSQ, is available from

C. Abaci, Inc., for $75 plus shipping/media charge.

-- C. Lawson clawson@math.jpl.nasa.gov

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

From: David Keaton <dmk@dmk.com>

Date: Wed, 3 Jun 92 10:34 MDT

**Subject: Re: Did Roundoff Cause Patriot Failure?**

It appears that several members of the Numerical Analysis mailing

list are confused. Would you please post the following message there

for me?

I have absolutely no connection with the government and am not a

distribution point for the Patriot missile bug report. I am just a

citizen letting people know how to get ahold of it. Please contact

the GAO to receive your report, not me. As far as I know, there is no

way to get it by email.

David Keaton

dmk@dmk.com

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

From: Stephen Nash <snash@gmuvax.gmu.edu>

Date: 5 Jun 92 15:03:00 EST

**Subject: Who was Raphson? (an answer)**

Who was Raphson? (an answer)

Many thanks to those of you who responded with suggestions. The popular

answer, by the way, is that "Raphson was Newton's programmer." (This answer

has been attributed to Doug Wilde of Stanford University.) You can decide for

yourself the accuracy of this statement.

Newton studied a number of methods for finding roots of polynomials. (Many of

these results were not published by Newton, but are now available in [N].

Whiteside, the editor, has provided detailed tables of contents and footnotes.

I have found these volumes to be a remarkable resource.) In late 1664 (?)

Newton examined existing algorithms due to Viete and Oughtred [N, v. 1].

(These are linearly convergent methods that find the root one digit at a

time; for details see [G, p. 66].) In early 1665 (?) Newton discovered the

secant method [N, v. 1]. The derivation appears to be based on geometric

reasoning, although Newton does not include a diagram.

In June 1669 (?) in a manuscript entitled "De Analysi Per Aequationes

Infinitas" Newton derives his version of what is now called the Newton-Raphson

method [N, v. 2]. The derivation is analytic, based on a linearization of a

higher-order polynomial. Newton solves a cubic equation (y^3 - 2y - 5 = 0). A

few pages later Newton uses his technique symbolically to develop a power

series expansion for the root of an equation. His comments seem to suggest

that he was aware of his method's quadratic convergence rate, but this result

is not stated explicitly. Newton also points out that you could use a

quadratic approximation and ``in that way you will gain twice as many figures

each time.''

Although it appears that Newton discovered this method independently,

Whiteside comments that "this method of resolving numerical equations has a

long manuscript history, and its essential structure was known to the

fifteenth-century Arabic mathematician al-Kasi." (Whiteside goes on to give

further background information.)

Joseph Raphson F.R.S. (1648-1715) published a variant of Newton's method in

"Analysis Aequationum universalis ..." (1690). (I have not seen this work; the

original is in the British Library, London.) Raphson had seen Newton's

manuscript. The two methods are equivalent, but Raphson did not realize this.

According to [B], "Newton laboriously derives a new cubic equation each time,

linearizes it as though it were unique, and then solves it to find the

residual for that equation; it is only at the end of the process that all

these residuals are added together to solve the original equation. Raphson, on

the other hand, systematically writes a `theorem' or `canon' for a general

cubic equation to find the residual x to be added to any guess g. ... This can

be seen as exactly the same as the modern-day procedure ... Both methods must

give the same increments ... thereby proving that they are the same method,

but Raphson has taken Newton's and given it a form that is at the same time

more general as well as more convenient." (Another discussion of Raphson'

contribution can be found in [W].)

There remains the question of who generalized this method to systems of

nonlinear equations. G.J. Tee speculated that this may have been done by Gauss

in his "Theoria Motus Corporum Coelestium in Sectionibus Conicus Solem

Ambientum" (1809). A translation of this work is available from Dover. I have

not yet looked at it.

[B] N. Bicanic and K.K. Johnson, "Who was '-Raphson'?" Int. J. Num. Meth.

Engng. 14 (1979), pp. 148-152.

[G] H.H. Goldstine, "A History of Numerical Analysis from the 16th through

the 19th Century," Springer Verlag (1977).

[N] Isaac Newton, "The Mathematical Papers of Isaac Newton (7 volumes),"

edited by D.T. Whiteside, Cambridge University Press (1967-1976).

[W] R. Wait, "The Numerical Solution of Algebraic Equations," Wiley (1979).

Stephen Nash

George Mason University

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

From: Craig Barratt <craig@ISL.Stanford.EDU>

Date: Mon, 08 Jun 92 00:39:07 -0700

**Subject: Overlaying Postscript Figures with LaTeX Fragments**

This is somewhat outside NA-Net's scope, but many subscribers might be

interested.

I have written some LaTeX macros (PsFrag) that make it easy to overlay

postscript figures with fragments of LaTeX. I use these macros to place

nice LaTeX equations and math symbols on top of postscript figures.

More precisely, the PsFrag macros allow specific pieces of postscript

text in a postscript figure (included via \epsfbox or \special) to be

replaced with arbitrary fragments of LaTeX. When your document is

latex'ed and dvips'ed, each piece of postscript text is replaced by

the LaTeX text.

The postscript file might be produced, for example, by xfig, idraw,

matlab, xmath, etc. Each string displayed by postscript's show operator

is a candidate for replacement by LaTeX text, math symbols, equations,

pictures etc. For example, you can include a matlab plot in a LaTeX

document with the title, axis labels, and legend generated by LaTeX.

The LaTeX fragments can be optionally rotated, scaled, and repositioned

relative to the text being replaced. The LaTeX fragments automatically

track the postscript text position as the scaling and offsets of the

\special or \epsfbox are changed.

PsFrag is available via anonymous ftp from isl.stanford.edu. After

logging in, cd to the directory pub/boyd/psfrag, and set binary mode.

Get the compressed tar file psfrag.tar.Z, uncompress it, and tar xvf it:

uncompress psfrag.tar.Z

tar xvf psfrag.tar

See the files README, USAGE, INSTALL for detailed information.

Note: PsFrag uses ghostscript (gs) and assumes that your dvi to ps driver is

Tomas Rokicki's dvips. You will need both of these programs to use PsFrag.

Craig Barratt

craig@isl.stanford.edu

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

From: Eric Grosse <ehg@research.att.com> 908-582-5828

Date: Mon, 8 Jun 92 12:50 EDT

**Subject: SISSC Table of Contents Online**

Thanks to the efforts of Bernadetta DiLisi, you can now do a keyword

or author search in the table of contents of the SIAM Journal on

Scientific and Statistical Computation, issues 1:1 through 13:1.

For example,

mail netlib@research.att.com

find Petzold stiff from siam

yields

Automatic Selection of Methods for Solving Stiff and Nonstiff

Systems of Ordinary Differential Equations

Linda Petzold

Pgs. 136-148

SISSC 4:1 Mar 1983

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

From: George D. Byrne <GDBYRNE%ERENJ.BITNET@pucc.Princeton.EDU>

Date: Wed, 03 Jun 92 09:33:05 EDT

**Subject: New Book by Bryne and Schiesser**

We are pleased to announce the publication of the book "Recent

Developments in Numerical Methods for ODEs/DAEs/PDEs," ISBN 981-02-0557-0,

which was edited by George D. Byrne and William E. Schiesser. The publisher is

World Scientific Publishing Company, Suite 1B, 1060 Main Street, River Edge,

NJ 07661, telephone 201/487-9655, rush orders telephone 201/487-9656,

and FAX 201/487-9656.

The book is a collection of papers presented at the November 1990

American Institute of Chemical Engineers Annual Meeting in a session by the

same name as the title. One objective of the book and of the session was to

bring people active in numerical methods in contact with those who use them.

The contents of the book are as follows:

"An Overview of Recent Developments in Numerical Methods and Software for

ODEs/DAEs/PDEs," by G. D. Byrne and W. E. Schiesser.

"Experiments with an Ordinary Differential Equations Solver in the

Parallel Solution of Method of Lines Problems on a Shared Memory Parallel

Computer," by D. K. Kahaner, E. Ng, W. E. Schiesser, and S. Thompson.

"CRAYFISHPAK: A Vectorized Fortran Package to Solve Helmholtz Equations,"

by R. A. Sweet.

"Experiments with an Adaptive H-, R-, and P-Refinement Finite Element

Method for Parabolic Systems," by J. E. Flaherty and Y. Wang.

"Incomplete Block Factorization Preconditioners: An Implementation for

Block Tridiagonal Systems," by D. E. Salane.

"Fast Generation of Weights in Finite Difference Formulas," by Bengt

Fornberg.

"Numerical Methods for Boundary Value Problems in Differential-Algebraic

Equations," by U. M. Ascher and L. R. Petzold.

"The Solution of a Co-Polymerization Problem with VODE," by G. D. Byrne.

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

From: W. E. Schiesser <WES1@SSCVX1.SSC.GOV>

Date: Wed, 3 Jun 1992 15:23:44 -0500 (CDT)

**Subject: Two New Books**

Two new books are now available from Academic Press

(1) "The Numerical Method of Lines Integration of Partial Equations",

W. E. Schiesser, ISBN: 0-12-624130-9

(2) "Dynamic Modeling of Transport Process Systems", C. A. Silebi and

W. E. Schiesser, ISBN: 0-12-643420-4

Academic Press, Inc.

1250 Sixth Avenue

San Diego, CA 92101 USA

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

From: Iain Duff <ISD@IBM-B.RUTHERFORD.AC.UK>

Date: Thu, 04 Jun 92 09:55:08 BST

**Subject: CERFACS Annual Report by FTP**

The 1990-91 CERFACS Annual Scientific Report is available from CERFACS

by anonymous ftp. In order to get this report which covers all aspects

of CERFACS Scientific activity, you should do the following:

1) TYPE :

ftp orion.cerfacs.fr

OR

ftp 138.63.200.33

2) LOGIN :

anonymous

3) PASSWORD :

your email address

4) Select directory:

cd pub/REPORTS/Scient_rep/Cerfacs

5) Receive appropriate file:

bin

get PSScRep91.tar.Z

6) On your machine you must uncompress the ".Z" file

and then tar the resulting tar file. Instructions

for printing the resulting ps files will be found in

the README_PS file.

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

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

Date: Thu, 4 Jun 92 14:22:28 +1000

**Subject: CTAC93 Meeting in Australia**

Preliminary Announcement: CTAC93

CTAC93 is the 8'th biennial Conference of the Special Interest Group in

computational techniques and applications of the Applied Mathematics

Division of the Australian Mathematical Society.

Venue: School of Mathematical Sciences

The Australian National University,

Canberra, A.C.T.

Dates: 5-7'th July, 1993.

Organising Committee:

Director: Mike Osborne (Maths, ANU)

Treasurer: Steve Roberts (Maths, ANU)

Secretaries: Henry Gardiner (Th. Phys., ANU), hjg105@csc.anu.edu.au

Dave Singleton (Supercomputer Facility, ANU),

singleton_d@laplace.anu.edu.au

Dave Stewart (Maths, ANU), des@thrain.anu.edu.au

Jerrard Barry (ANSTO, Chairman of CTAC)

Basil Benjamin (Math, USA)

Kevin Burrage (Maths, UQ)

Frank De Hoog (DMS, CSIRO)

Alan Easton (Maths, SIT)

Clive Fletcher (Mech. Eng., SU)

Bob Gingold (Supercomputer Facility, ANU)

Linsey Hood (ANU and TMC)

Invited Speakers:

Anthony Cooper (Lausanne) Stability calculations in MHD and Plasmas.

Charles Elliott (Sussex) Multiphase flow problems.

David Green (ANU) Neural nets, L-systems, and complex systems applications.

Andreas Griewank (Argonne) Automatic differentiation of algorithms.

Steve McCormick (U.C. Denver) Multilevel projection methods.

Joe Monaghan (Monash) Particle in cell methods.

Workshops: It is expected that several workshops will be associated with the

conference and will be held on July 8-9'th. Topics mooted include

`computational techniques in MHD and Plasma research', `high level languages

for distributed memory multiprocessors', and `numerical techniques in

optimization'.

Call for Papers: It is intended that this will be issued by November 1992.

Intending speakers will be asked to make preliminary versions of their

papers available for distribution at the conference. They will be notified of

procedures and recommended formats. Refereed Proceedings of CTAC conferences

are published.

Conference Information: An information file on the Conference,

`ctac93.info', is held in the ftp directory pub/CTAC3 on thrain.anu.edu.au

and is available for access by anonymous ftp (log in as anonymous and use

your email address as password).

Sponsors: These will include: The Australian National University, The British

Council, Cray Research (Australia).

Expressions of interest: Anyone wishing to be sent further information on

CTAC93 is requested to contact:

CTAC registration email: ctac-reg@thrain.anu.edu.au

School of Mathematical Sciences fax : 61+6 247 2347

Australian National University

PO BOX 4 Canberra

ACT 2601

Australia

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

From: Frank Plab <PNAW92@edinburgh.ac.uk>

Date: Tue, 9 Jun 92 0:32:43 WET DST

**Subject: Parallel Numerical Analysis Workshop `92: PROGRAM**

FINAL CALL FOR PARTICIPATION

Second Workshop

on

PARALLEL NUMERICAL ANALYSIS

sponsored by

Edinburgh Parallel Computing Centre

and Science and Engineering Research Council

cosponsored by

The Institute of Mathematics and its Applications

25-26 June 1992

University of Edinburgh

Scotland, UK

The Edinburgh Parallel Computing Centre is organizing a two day

``Workshop on Parallel Numerical Analysis'' in Edinburgh on 25 and 26

June this year for mathematicians and others interested in the numerical

aspects of parallel computing.

INVITED SPEAKERS:

Prof D.P. Bertsekas (Department of Electrical Engineering and Computer

Science, MIT, Cambridge, USA)

Prof Z. Zlatev (National Environmental Research Institute, Roskilde,

Denmark)

Prof L.C.W.Dixon (School of Information Sciences, Hatfield Polytechnic, UK)

Prof Morgan (Department of Civil Engineering, University of Swansea, UK)

WORKSHOP FEE (incl. lunches): \pounds 20

The Edinburgh Parallel Computing Centre (EPCC) is a multi-disciplinary

institution engaged in research into and commercial development of

parallel computing. It is home to a wide range of parallel computing

equipment, including: a 16K processor Connection Machine CM-200, a Meiko

Computing Surface with more than 400 T800 transputers; the UK Grand

Challenge machine, which contains 64 i860/T800 hybrid nodes; and 64x64

AMT DAP. EPCC has a full-time staff of over 35, and a large number of

associates in computer science, physical and mathematical sciences.

For an electronic registration form and a copy of the preliminary

program, please contact:

PNAW92

c/o Frank Plab

Edinburgh Parallel Computing Centre

James Clerk Maxwell Building

University of Edinburgh

Mayfield Road

Edinburgh EH9 3JZ

Phone: 031-650 5818/5042 (UK), +44-31-650 5818/5042 (international)

Fax: 031-650 6555 (UK), +44-31-650 6555 (international)

E-mail: PNAW92@ed.ac.uk

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

From: Petter Bjorstad <Laila.Liseth@ii.uib.no>

Date: Thu, 4 Jun 1992 09:41:11 +0200

**Subject: Positions at University of Bergen**

POSITIONS AVAILABLE AT THE UNIVERSITY OF BERGEN

UNIFOB, University of Bergen has 5 vacant positions

at Para//ab - Laboratory for parallel computing

MASSIVELY PARALLEL COMPUTING

Para//ab was established in 1988 and represents the centre of effort of

research in and application of parallel computing at the University of

Bergen. Para//ab is operated by the Department of Informatics, and the

laboratory is recognised as one of the leading laboratories in Europe

in information technology.

Para//ab now wishes to increase its activities within supercomputing, and

announces the following vacant positions:

- 2 Senior Scientists/Post Doctorate

- 2 Stipendiate/Doctorate

- 1 Scientist

The positions are organised under the UNIFOB foundation. Those accepted

for the positions will take part in work funded by the Norwegian

research councils NTNF and NAVF together with industrial partners to

convert applications to parallel architectures and contribute to

algorithm development. The accepted candidates will also be expected

to contribute with active support to external users of the laboratory's

equipment. The Doctoral candidates will take part in para//ab projects

as part of their compulsory activities.

Qualifications:

SENIOR SCIENTIST/POST DOC. must have Norwegian or other foreign

doctoral degree within the natural sciences. The applicants must be

able to document skills and experience with the use of advanced

computers in scientific computation. The first position will involve

a responsibility for system applications for the laboratory's parallel

computers, and active involvement in research projects. The second

position will be mainly involved with the laboratory's industrial

project "Massively parallel algorithms for reservoir simulation"

STIPENDIATE must be qualified for a doctoral programme at the

Department of Informatics, University of Bergen. The student shall

carry out his/her studies in problem areas within parallel

computation.

SCIENTIST must have qualifications equivalent to Cand.

Scient./Siv.ing. (Master of Science) and documented experience and

competence in the use of advanced computers. The working area will be

application development for massively parallel computers, external user

support and project activities where effective use of parallel

computers is in focus.

The three scientist positions are available for a period of three

years. The stipendiate positions are for 4 years. Further details of

the positions can be obtained from Professor Petter Bjorstad, Dept. of

Informatics, tel. +47 5 54 41 71.

Applications, including details of educations and earlier experience, together

with references and certificates, should be sent to: The University of

Bergen, Personell Dept., N-5020 Bergen, by 15. June 1992.

Scientific works should be sent direct to: Dept. of Informatics, High

Technology Centre, N-5020 Bergen by the same date.

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

From: Richard A. Brualdi <brualdi@imafs.ima.umn.edu>

Date: Fri, 5 Jun 92 12:26:09 CDT

**Subject: Linear Algebra and its Applications**

Below are the contents of Volume 172 of LAA. The contents of LAA

beginning with Volume 150 as well as information on the current

special issues of LAA are available from the ILAS Information

center. They can be obtained as follows:

Send an email message to listserv@technion.bitnet (or

listserv@technion.technion.ac.il) with the commands in

the mail body of the message:

get LAA 91-92

get LAA SPECIAL

The files will then be sent to you as an email message.

The files can also be obtained by anonymous FTP.

LAA Contents Volume 172, July 15, 1992

(Proceedings of the NIU Conference)

David Carlson (San Diego, California), Daniel Hershkowitz, and

Dafna Shasha (Haifa, Israel)

Block Diagonal Semistability Factors and Lyapunov Semistability

of Block Triangular Matrices 1

Y. P. Hong and C.-T. Pan (DeKalb, Illinois)

A Lower Bound for the Smallest Singular Value 27

Kenneth D. Clark (Research Triangle Park, North Carolina)

Decomposition of Hessenberg DAE Systems to State Space Form 33

Marcin Paprzycki (Odessa, Texas)

Comparisons of Gaussian Elimination Algorithms on a Cray Y-MP 57

Shmuel Friedland (Chicago, Illinois)

Lower Bounds for the First Eigenvalue of Certain *iM-Matrices

Associated With Graphs 71

Richard E. Faulkenberry (North Dartmouth, Massachusetts)

The Continuous Kernel of a Nonsquare Rational Matrix Function 85

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

Nested Range Conditions for *iL*iU Factorizations of Integer Matrices 97

Daniel L. Boley (Minneapolis, Minnesota), Tong J. Lee, and

Franklin T. Luk (Ithaca, New York)

The Lanczos Algorithm and Hankel Matrix Factorization 109

Leonid Gurvits (New York, New York), Leiba Rodman

(Williamsburg, Virginia), and Tamir Shalom (New York, New York)

Controllability and Completion of Partial Upper Triangular

Matrices Over Rings 135

Richard A. Brualdi and Geum-Sug Hwang (Madison, Wisconsin)

Generalized Transitive Tournaments and Doubly Stochastic Matrices 151

James Nagy (Raleigh, North Carolina) and Robert J. Plemmons

(Winston-Salem, North Carolina)

An Inverse Factorization Algorithm for Linear Prediction 169

S. L. Chung, F. B. Hanson, and H. H. Xu (Chicago, Illinois)

Parallel Stochastic Dynamic Programming: Finite

Element Methods 197

D. Calvetti (Hoboken, New Jersey) and L. Reichel (Kent, Ohio)

A Chebychev-Vandermonde Solver 219

James R. Bunch and Ricardo D. Fierro (La Jolla, California)

A Constant-False-Alarm-Rate Algorithm 231

Thomas J. Laffey and Eleanor Meehan (Dublin, Ireland)

An Extension of a Factorization Theorem of Wedderburn to

Matrix Rings 243

Richard A. Brualdi and Hyung Chan Jung (Madison, Wisconsin)

Maximum and Minimum Jump Number of Posets From Matrices 261

D. Y. Hu (Lexington, Kentucky) and L. Reichel (Kent, Ohio)

Krylov-Subspace Methods for the Sylvester Equation 283

G. S. Ammar (DeKalb, Illinois), W. B. Gragg (Monterey, California),

and L. Reichel (Kent, Ohio)

Downdating of Szego@a3 Polynomials and Data-Fitting Applications 315

Roger A. Horn (Baltimore, Maryland) and Roy Mathias (Williamsburg, Virginia)

Block-Matrix Generalizations of Schur's Basic Theorems on

Hadamard Products 337

P. Amodio and L. Brugnano (Bari, Italy)

Parallel Factorizations and Parallel Solvers for Tridiagonal Linear

Systems 347

Author Index 365

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

End of NA Digest

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

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