- Today's Editor:
- Cleve Moler
- The MathWorks, Inc.
- moler@mathworks.com

- Meta-discussion of NA Digest
- A Function Equation
- C-codes for GEVD and SVD
- Question on Numerical Methods for ODEs
- Iterative Least Squares
- Backwards Heat Equation
- Eigenvalue of Large, Banded Toepliz Matrices
- Stability of Recurrence
- A Matrix Eigenvalue Problem (Solution #1)
- A Matrix Eigenvalue Problem (Solution #2)
- A Matrix Eigenvalue Problem (Solution #3)
- Interpolation on a Square Grid (Solution)
- New Book from IEEE Press
- Multigrid Workshop In Australia
- Bay Area NA Day
- Positions at IBM Watson Research Center
- Ph. D. Scholarship in Norway
- Benin Conference in Nigeria
- Contents, SIAM Optimization
- Contents, Linear Algebra and its Applications

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

From: Michael C. Grant <mcgrant@rascals.stanford.edu>

Date: Sat, 26 Feb 1994 16:26:53 -0800

**Subject: Meta-discussion of NA Digest**

> From: Tom Scavo <scavo@cie.uoregon.edu>

> Date: Sun, 20 Feb 94 11:53:03 -0800

> Subject: Re: A Meta-answer

> I agree with Arne. An interactive forum along the lines of the

> Usenet newsgroup sci.math.num-analysis would be more productive.

Then why not read sci.math.num-analysis? I wish more people would

actively participate in that newsgroup. I would hope that Usenet

access is not a problem for .edu sites, at least. Perhaps similar

newsgroups (or their equivalent) can be created on Compuserve, AOL,

Prodigy, etc. etc., with their contents automagically shared.

> In fact, I think NA Digest and sci.math.num-analysis would

> benefit greatly from each other. I know that some mailing lists

> are automatically gated into the appropriate newsgroup. Maybe

> that could be done in the case of NA Digest. I, for one, would

> welcome the change.

sci.math.num-analysis is small enough that an automatic

news-to-mailing-list gateway might be practical. Those people with

mail readers that can automatically extract such messages from their

inbox and move them to a separate folder for later perusal will find

this quite convenient; MH has such a facility called 'slocal' that

might work with other mail handlers (I haven't used it though).

> Just look how long it's taken to get these three related messages

> to the list. In a newsgroup, it's not uncommon for a thread to

> generate the same reponse in a matter of hours.

That's why this digest is much better suited for things such as

conference announcements, employment positions, and other general

interest announcements for which no feedback (to the Digest) is

necessary.

Michael C. Grant

mcgrant@rascals.stanford.edu

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

From: Frank Stenger <stenger@sinc.cs.utah.edu>

Date: Sun, 27 Feb 1994 11:35:19 -0700

**Subject: A Function Equation**

An unsolved problem:

Let f be a positive, decreasing function defined on [0,1], such that

f(0) = 1, f(1) = 0, and such that for all x on [0,1], we have

f((1 - (f(x))^2)^(1/2)) = 1-x, and f(f(x)) = x.

Can we find an explicit functional expression for f?

Frank Stenger

Department of Computer Science

University of Utah

Salt Lake City, Utah 84112

E-mail: stenger@cs.utah.edu

Phone: (801) 585-SINC

Fax: (801) 581-5843

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

From: Comon Pierre <comon@mimosa.unice.fr>

Date: Mon, 28 Feb 1994 11:03:28 GMT

**Subject: C-codes for GEVD and SVD**

Could anyone send me C-codes for GEVD and SVD.

The library packages I have do not contain these tools.

Thanks, comon@mimosa.unice.fr

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

From: Stanly Steinberg <stanly@deepthought.unm.edu>

Date: Mon, 28 Feb 94 09:32:04 MST

**Subject: Question on Numerical Methods for ODEs**

I am looking for information on discretizations of a system of

ordinary differential equations of the form

dx/dt = A x + B x

where the system with B = 0 is stiff and simple while the system

for A = 0 is not stiff and complex.

Stanly Steinberg

stanly@math.unm.edu

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

From: James F. Epperson <epperson@slick.math.uah.edu>

Date: Wed, 2 Mar 94 14:52:14 CST

**Subject: Iterative Least Squares**

Do there exist algorithms for solving sparse, structured

least squares problems that are analogous to, say, SOR or

Gauss-Seidel for the linear systems problem? What am looking

for is a way to solve the normal equations (A^T)Ax=(A^T)f without

forming (A^T)A, or to do an (approximate) QR decomposition of A

without all the fill-in that would ordinarily occur.

Thanks in advance

Jim Epperson

Mathematical Sciences Dept.

Univ. of Alabama-Huntsville

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

From: James F. Epperson <epperson@slick.math.uah.edu>

Date: Wed, 2 Mar 94 14:56:04 CST

**Subject: Backwards Heat Equation**

To save me and a colleague from the embarassment of

perhaps re-inventing the wheel, could someone direct

me to a reference for what might be considered the

"state-of-the-art" for solving the backwards heat

equation?

Thanks in advance,

Jim Epperson

Mathematical Sciences Dept.

Univ. of Alabama-Huntsville

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

From: Fred Kus <fred@blas.cis.mcmaster.ca>

Date: Fri, 4 Mar 1994 14:40:26 -0500

**Subject: Eigenvalue of Large, Banded Toepliz Matrices**

Hi,

A researcher here in Chemistry asked about software to solve for the

extreme eigenvalues/vectors of a symmetric, narrow banded Toeplitz matrix of

size n => 10**6. The band routines in Lapack as well as several Lanczos

codes that were tried, did not seem suitable for such a large matrix. Also,

they do not take advantage of the Toeplitz structure A(i,j) -> A(|i-j|)

to reduce the memory required.

Any information and/or software to deal with this problem would be greatly

appreciated.

Thanks

Fred

Fred W. Kus INTERNET: fred@mcmail.CIS.McMaster.CA

Computing & Information PHONE: (905) 525-9140 ext. 24160

Services FAX (905) 528-3773

McMaster University A. N. Bourns Bldg. Rm 131C

Hamilton, Canada L8S 4M1

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

From: Simon Wang <MEG1839@v2.qub.ac.uk>

Date: Sat, 5 Mar 94 4:57 GMT

**Subject: Stability of Recurrence**

Stability of Recurrence

Please help me consider the stability problem of the following

recurrence:

A X_{n+1} + B Y_{n+1} = C X_n + D Y_n (1)

where A, B, C and D are known constant square matrices (nonsingular), Y and

Z are vectors.

My question is: if the following recurrences

A X_{n+1} = C X_n (2)

B Y_{n+1} = D Y_n (3)

are stable, can we draw the conclusion that the recurrence in (1) must be

stable? If so, any condition required?

Thanks for your time.

Simon Wang

Email: MEG1839@V2.QUB.AC.UK

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

From: Garry Tee <tee@mat.auckland.ac.nz>

Date: Mon, 28 Feb 1994 12:35:09 +1200

**Subject: A Matrix Eigenvalue Problem (Solution #1)**

>On Wed, 16 Feb 94 09:25 CST, Richard Luczak <luczak@nag.com> asked

>in NA Digest, V. 94, # 8:

>

>> Let A be a tridiagonal matrix of the form

>> -2 2

>> 1 -2 1

>> . . .

>> 1 -2 1

>> 2 -2

>> What is the formula for all eigenvalues of matrix A?

Let A be of order n>1.

Consider the vector v[k] with elements v[k]_j = cos((k-1)(j-1)Pi/(n-1)),

j = 1,...,n. It is readily verified that v[k] is an eigenvector of A with

eigenvalue m_k = -4 sin^2((k-1)Pi/(2n-2)). (Note that v[k]_1 = 1, and

hence v[k] is non-null). For k = 1,...,n this gives n distinct eigenvalues:

0 = m_1 > m_2 > ,,, > m_n = -4.

Hence, those are all the eigenvalues of A, with eigenvectors v[1],,...v[k].

Garry J. Tee.

Department of Mathematics, University of Auckland, Auckland, New Zealand.

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

From: Di Benedetto <DIBEN@novell.dima.unige.it>

Date: Mon, 28 Feb 1994 17:14:57 GMT+1

**Subject: A Matrix Eigenvalue Problem (Solution #2)**

On Wed, 16 Feb 94 09:25 CST, Richard Luczak <luczak@nag.com> asked

in NA Digest, V. 94, # 8:

> Let A be a tridiagonal matrix of the form

> -2 2

> 1 -2 1

> . . .

> 1 -2 1

> 2 -2

> What is the formula for all eigenvalues of matrix A?

On Mon, 21 Feb 1994 12:35:37 --100, Christian Brechbuehler

<brech@vision.ethz.ch> made in NA Digest, V. 94, # 9, the following

conjecture:

> Let A be n by n with n > 1.

> Eigenvector j (not normalized) has the components

> cos(i j Pi/(n-1)),

> where 0 <= j < n

> 0 <= i < n.

>

> Arbitrarily picking the first row of A, we have the Eigenvalues

> 2(cos(j Pi/(n-1)) - 1).

The conjecture is true, here is a possible way to prove it.

Writing A = T - 2 I , it suffices to compute the eigensystem of the

tridiagonal matrix

0 2

1 0 1

1 0 1

.....

T = ..... ,

.....

1 0 1

1 0 1

2 0

which is Toeplitz except the first and the last row.

The eigenvalue problem for T can be treated in a similar way as in

W.F.Trench, "On the eigenvalue problem for Toeplitz band matrices"

(Lin. Alg. Appl. 64, pp.199-214)

by expressing the relation (T - l I) u = 0 as a difference equation:

u(k+2) - l u(k+1) + u(k) = 0, k = 0,...,n-3

with the boundary conditions

2 u(1) = l u(0), 2 u(n-2) = l u(n-1).

If z is a root of the characteristic equation

z^2 - l z + 1 = 0 (whence l = z + 1/z)

then u(k) has the expression

u(k) = a1 z^k + a2 / z^k,

where a1 and a2 are nonzero solutions of the linear system

(2 z - l) a1 + (2/z - l) a2 = 0

z^(n-2) (2 - l z) a1 + z^(2-n) (2 - l/z) a2 = 0,

which takes into account the boundary conditions.

Substituting l = z + 1/z in the determinant d of such linear

system and solving d = 0 with respect to z, the formulae

conjectured by Brechbuehler are easily derived.

Fabio Di Benedetto

Dip. di Matematica - Univ. di Genova

via L.B.Alberti 4

I - 16132 Genova (Italy)

e-mail: dibenede@dima.unige.it

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

From: Katalin Balla <@helios.edvz.univie.ac.at,@HUEARN.SZTAKI.HU:H153Bal@HUELLA.BITNET>

Date: 1 Mar 94 18:31:58 +0100

**Subject: A Matrix Eigenvalue Problem (Solution #3)**

In Na-Digest 94, N9 , Christian Brechbuechler (brech@vision.ethz.ch)

proposed a conjecture that answers the question posed

by Richard Luczak (luczak@nag.com) a week earlier. The conjecture is true.

> Let A be a tridiagonal matrix of the form

> -2 2

> 1 -2 1

> . . .

> 1 -2 1

> 2 -2

> What is the formula for all eigenvalues of matrix A?

< 2(cos(j Pi/(n-1)) - 1).

<They are in descending order for increasing j. The largest Eigenvalue

<is 0, the smallest is -4, independent of n.

One can find the problem (for -A) with all details (eigenvectors, etc.)

as Example N5 in &3.3. (pp.264-266) in the book "Linear algebra and its

applications" by Pal Rozsa written in Hungarian (Linearis algebra es

alkalmazasai. Muszaki Konyvkiado, Budapest, 1976,ISBN 963 10 1278 4).

These two pages do not require any knowledge of Hungarian. Or, one can

write directly to the Prof. P. Rozsa, e-mail:

rozsa@euromath.vma.bme.hu (He knows about this message.) Katalin Balla

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

From: Jorgen Sand <datjs@diku.dk>

Date: Fri, 4 Mar 1994 13:56:07 +0100 (MET)

**Subject: Interpolation on a Square Grid (Solution)**

In last week's nanet-news T.R.Hopkins put forward a question concerning

interpolation on a square grid, where the values of the function and its

first order derivatives were known at the grid points. One possible solution

is to find the unique interpolating polynomium of the form:

p(x,y) = (a00+a10*x+a01*y+a11*x*y) + x^2*(a20+a30*x+a21*y+a31*x*y)

+ y^2*(a02+a12*x+a03*y+a13*x*y)

on each square. The 12 coefficients are listed below in case of the square

[0,1]x[0,1] and for the square [x1,x2]x[y1,y2] one may use

p((x-x1)/(x2-x1),(y-y1)/(y2-y1)).

a00=f11, (* the value of the function in (x1,y1) *)

a10=fx11, (* the value of the x-derivative in (x1,y1) *)

a01=fy11, (* the value of the y-derivative in (x1,y1) *)

a11=fy21-f22+f12+f21-fx11+fx12-f11-fy11,

a20=-2*fx11+3*f21-3* f11-fx21,

a30=fx21+2*f11+fx11-2*f21,

a21=-2*fx12+3*f22+3*f11-fx22+fx21+2*fx11-3* f21-3*f12,

a31=fx12+fx22-fx21-fx11+2*f21-2*f11+2*f12-2*f22,

a02=-2*fy11 -fy12-3*f11+3*f12,

a12=-fy22+fy12+2*fy11-2*fy21-3*f12+3*f11+3*f22-3*f21,

a03=-2 *f12+2*f11+fy12+fy11,

a13=-fy12+2*f21-2*f11+2*f12-2*f22+fy21+fy22-fy11]);

Jorgen Sand

Dept. of Comp.Sci.

Univ. of Copenhagen, Denmark

e-mail: datjs@diku.dk

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

From: Rajni Patel <rajni@ece.concordia.CA>

Date: Sat, 26 Feb 1994 14:15:20 -0500

**Subject: New Book from IEEE Press**

NEW from IEEE Press

NUMERICAL LINEAR ALGEBRA TECHNIQUES

FOR SYSTEMS AND CONTROL

Edited by

Rajni V. Patel, Concordia University

Alan J. Laub, University of California, Santa Barbara

Paul M. Van Dooren, University of Illinois, Urbana

With an extensive 35-page introduction, and 21 pages of

bibliography, this edited collection of 47 key papers incor-

porates over 15 years of intensive research in the field of

modern numerical linear algebra and its application to com-

putational problems in systems and control. The book illus-

trates the importance and rapid growth of this area of

research, and helps to focus attention on the directions

that future research should take. The introduction and

papers presented in the book also provide a thorough back-

ground for all current computer-aided control system

analysis and design software and, in particular, address the

following issues:

* How to assess numerical stability and conditioning

most effectively in numerical analysis.

* Efficient ways to translate system and control

ideas into reliable numerical algorithms.

* Using condensed forms to check controllability,

observability, and other properties of a model.

* The effect of model uncertainties on various numer-

ical properties of a given model.

* The most reliable algorithms for the key computa-

tional problems in linear system theory.

As the only collection of papers covering the broad scope of

numerical linear algebra in systems and control, this book

will be of interest to engineers and applied mathematicians

as well as others engaged in any aspect of control system

analysis and design.

The book contains the following chapters:

1. Introduction and Survey

2. General Numerical Issues in Control

3. Controllability, Observability, and Realizations

4. ``Closeness'' Problems

5. Frequency Response, Transfer Functions, Poles and

Zeros

6. Pole Assignment and Observer Design

7. Riccati, Lyapunov, and Sylvester Equations

8. Some Relevant Results from Numerical Linear Algebra

9. Bibliography

ORDERING INFORMATION:

NUMERICAL LINEAR ALGEBRA TECHNIQUES

FOR SYSTEMS AND CONTROL

edited by

Rajni V. Patel

Alan J. Laub

Paul M. Van Dooren

IEEE Control Systems Society Member Price: $45.00

Regular IEEE Member Price: $72.00

List Price: $89.95

Hardcover, 736 pp

IEEE Order #: PC0340-0

ISBN 0-7803-0443-8

The book can be ordered by telephone or fax:

Tel: 1-800-678-IEEE (in USA) or 908-981-0060

Fax: 908-981-9667

or by mail:

IEEE

Customer Service Department

445 Hoes Lane, P.O. Box 1331

Piscataway, NJ 08855-1331

USA

The book is also available at a slightly higher price from:

IEEE Technical Activities Brussels Office

13, Avenue de L'Aquilon

B-1200 Brussels

BELGIUM

Fax: 32.2.770.85.05

Phone: 32.2.770.22.42

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

From: Steve Roberts <steve@laplace.anu.edu.au>

Date: Mon, 28 Feb 94 14:54:25 +1100

**Subject: Multigrid Workshop In Australia**

Workshop on Multigrid and Multilevel Methods

School of Mathematical Sciences

Australian National University

18th - 22nd April 1994

Profs Jim Bramble and Steve McCormick will both be at the ANU

during the last two weeks of April. To take advantage of this

opportunity, we are planning to hold a workshop in which they

will be the major contributors. We plan to hold this workshop

during the week 18th - 22nd April. Jim will give

a series of talks describing some of his recent work on low

regularity results for multigrid methods and Steve is planning to

talk on algorithms and multigrid applications.

Other speakers will include

Zbigniew Leyk "Iterative methods for solving large nonsymmetric

systems of linear equations"

David Stewart "Multilevel methods for approximate inertial manifolds

(in large scale dynamical systems)"

Suely Oliveira "Parallel Multigrid for Mantle Convection"

David Singleton "Multigrid in data parallel on the Connection Machine"

Steve Roberts, "Multigrid methods applied to geometic evolution problems"

A knowledge of the Multigrid method to the level

of William Briggs' ``A Multigrid Tutorial'' will be assumed.

It is intended that other participants to the workshop will

have an opportunity to present

their work on multigrid methods, or perhaps at a more informal

level, present problems in which multilevel methods may be applied.

At present the format and content of the workshop is very fluid.

If you would like to attend the workshop, contact me (Steve Roberts,

address below) giving details of your interests and background.

We will try to arrange the main talks to suit the average background

of the audience. The format of the workshop will be as informal as

possible, with an emphasis on allowing interaction between the

participants at the workshop.

Steve Roberts

Mathematics Department, The Faculties Office: (61)(6) 249 4445

Australian National University Messages: (61)(6) 249 2908

Canberra ACT 0200 Fax: (61)(6) 249 5549

AUSTRALIA

E-mail: steve.roberts@maths.anu.edu.au

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

From: John Strain <strain@math.berkeley.edu>

Date: Wed, 2 Mar 1994 09:15:54 -0800

**Subject: Bay Area NA Day**

Bay Area Numerical Analysis Day at Berkeley

Saturday, 26 March 1994

Everyone is invited!! Bay Area Numerical Analysis Day

will be held on the UC Berkeley campus on Saturday,

26 March 1994. Young Bay Area numerical analysts will

speak on their research. It will also be an excellent

opportunity to meet colleagues.

The meeting will begin at 9:30 am and finish up about

4:00, with a Chinese banquet at 6:30 pm, costing $20.

A second announcement with details will follow shortly.

-- John Strain

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

From: Erling Pytte <pytte@watson.ibm.com>

Date: Fri, 4 Mar 94 10:01:25 EST

**Subject: Positions at IBM Watson Research Center**

The IBM T.J. Watson Research Center have several positions in the area

of Computational Science. Intellectual power and scientific excellence

are the primary criteria, but affinity for and ability to use parallel

computers will be a valued tool. Among the resources available is a

128-way SP1 (128 RISC6000 with a fast switch for serial or parallel use).

Applications with resumes, list of publications, and references should be

sent to Dr. Erling Pytte, IBM T.J. Watson Research Center, P.O. Box 218,

Yorktown Heights, NY 10598.

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

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

Date: Sat, 5 Mar 1994 11:16:22 +0100

**Subject: Ph. D. Scholarship in Norway**

A Ph.D scholarship supported by the Norwegian Research Council,

is available immediately.

The Ph.D. student will perform research in scientific computing at the

department's laboratory for parallel computing (Para//ab).

The successful candidate must document strong knowledge

in mathematics and computer science.

For more information please contact:

professor Petter E. Bj{\o}rstad,

Institutt for Informatikk,

H{\o}yteknologisenteret,

Universitetet i Bergen,

N-5020 Bergen.

Phone: +47-55544171

E-mail: Petter.Bjorstad@ii.uib.no

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

From: John Pryce <pryce@rmcs.cranfield.ac.uk>

Date: Wed, 2 Mar 94 15:40 BST

**Subject: Benin Conference in Nigeria**

REPORT ON BENIN CONFERENCE, NIGERIA 1994

by John Pryce and Alastair Spence

The 24th - 28th January 1994 saw the Sixth International Conference on

Scientific Computing at the University of Benin (Uniben), Nigeria, directed

as were the previous conferences by Professor Simeon Ola Fatunla, head of

the department of Mathematics and Computer Science. It was attended by

over fifty delegates from Nigeria and by eight overseas visitors.

The organizing committee had chosen Parallel Computation as a main theme of

the conference in view of its importance to the computational needs of the

Nigerian oil industry. The venue was the main Auditorium of the

university. The opening ceremony was attended by senior figures of the

university and of the state government. Unlike previous conferences no

representatives of Federal government were present - this was one sign of

the unsettled political situation in the country. The keynote addresses

included John Pryce on "Scientific computing - key to an enduring

technology?" who emphasized that while computing is essential to high

technology, teaching basic technical skills (what in the UK are generally

called Do-It-Yourself) so that they are natural everyday activities of the

ordinary man and woman, is vital to an enduring technology. Also Dr Chris

Phillips gave a lucid and "low-tech" introduction to "What parallel

computing is all about". Unfortunately Prof Ezeilo, President of the

Nigerian Mathematical Society, and billed to give a keynote address, was

unable to be present.

The overseas visitors gave mainly survey talks on their specialist areas.

Willy Govaerts (University of Gent, Belgium) spoke on Bordered Matrix

Methods in studying Bifurcations of Large Dynamical Systems; Rolf Jeltsch

(ETH, Zurich, Switzerland) on a Truly Multi-dimensional Scheme for the

Euler Equations of Gas Dynamics; Choi-Hong Lai (University of Greenwich,

UK) on Domain Decomposition Methods and Massively Parallel Processing;

Marco Marletta (University of Leicester, UK) on Numerical Solution of

Hamiltonian System Eigenvalue Problems; Chris Phillips (University of

Newcastle, UK) on Parallel Implementation of Conjugate Gradient-Type

Methods; John Pryce (RMCS, Shrivenham, UK) on Test Packages for

Mathematical Software with a Sturm-Liouville Test Set as an example; Roger

Sidje (Ivory Coast, and Irisa, Rennes, France) on Krylov Subspace Methods

for Markov Processes; Alastair Spence (University of Bath, UK) on

Eigenvalues of Block Matrices arising from Discretizations of the Navier

Stokes Equations.

The talks by local researchers were again mostly of high quality, and

perhaps the best local talk was from Prof Mrs Oni of Ibadan theoretical

physics department who tackled a difficult and important problem from the

oil industry: of devising theoretically well-founded methods for extracting

more information from seismic survey data than is done at present. It was

good to see how many of the speakers were young. There was a welcome

increase in the number of numerical methods that were backed up by

numerical experiments and performance comparisons. The 'locally produced'

talks included, as one would expect, a good proportion from Professor

Fatunla's own school on methods for ODE's but went well beyond this to

problems of control, mathematical programming, combustion theory and

queuing theory. For the first time there were also (mainly expository)

talks on mainstream computer science topics such as topological sorting and

the timetabling problem. As usual, many final-year mathematics students

came to form an enthusiastic addition to the audience, and also attended a

Matlab tutorial, at which one woman student was heard to say "Mmm, I begin

to like this package".

A new feature was a four day Software Engineering Workshop held the week

prior to the Conference. This was a fairly informal event at which Simeon

Fatunla and John Pryce presented the basics of the engineering approach to

software development, to an audience of around twenty, the majority being

from commerce and industry. On the day following the workshop, Willy

Govaerts gave a series of lectures on the theory and uses of numerical

continuation and bifurcation computations.

The need for such training had been emphasized at the 1992 conference. The

workshop was full of discussion, interaction and controversy and a whole

day was given over to delegates presenting their own experiences. Plans

for a follow-up course with more professional facilities and course

material are in hand.

The conference booklet was professionally produced (it was interesting to

see a general move from LaTeX to Wordperfect for document preparation) with

abstracts and full names and addresses of participants. For the first time

it also contained maps of Uniben, Benin City and Nigeria and also - a

valuable addition - the membership of the local organization committees who

put in many hours of work before and during the conference to make it run

smoothly within tight constraints on budget and equipment. It is invidious

to single out names but especially obvious to us visitors were the efforts

of Dr David Igbafe of the reception committee, Dr Frank Otunta who chaired

the latter, and of Dr Victor Aladesula who was on hand punctually each

morning for nearly two weeks to transport us from our NNPC accommodation to

the workshop and conference venue, as well as his wife who also gave freely

of her time.

Most of the overseas visitors (not all owing to lack of space) were

accommodated courtesy of the Nigerian National Petroleum Corporation (NNPC)

at its guesthouse, where we were very comfortable and the menu included

grasscutter (a local animal related to the porcupine) and other varieties

of "bush meat" on demand. We appreciated the unobtrusive and efficient

service of the guesthouse reception staff. The local museum and art

gallery, and the Palm Research Institute (and its palm wine) were sampled

as usual, and the visitors explored the Benin city market with the help of

local staff and their wives to negotiate for souvenirs.

Comparing this with previous conferences one can report both good news and

bad news.

The bad news is that the prevailing political uncertainty and the apparent

absence of a coherent policy for higher education continues to leave the

universities in financial decline. One talented colleague from a

neighbouring university told me how his campus had been without national

grid electricity for six months of the last academic year owing to

inability to pay its electricity bill. Obviously, in such straits, other

necessities of academic life such as purchase of up-to-date international

journals have become unattainable luxuries.

The good news is that there is clearly a core of people who are determined

to carry on come what may and who are extending their locally based

activities. The last two conference Proceedings have been edited, typeset

and printed locally. Professor Fatunla's text "Fundamentals of Fortran

Programming" (see endnote) appeared in November, again typeset and printed

locally. Marketed by the African arm of Oxford University Press it has

already achieved a wide sale in Nigeria. Mr Kayode Ojoko, an entirely

Nigeria-educated civil engineer and software writer who runs a successful

engineering consultancy in Lagos, has demonstrated his structural analysis

Software at the 1992 conference and returned this year to show the

increasing range and sophistication of his products. Necessity as always

is proving to be the mother of invention and it is from such local

technical mastery and initiatives, as much as on any outside help, that the

technological progress of Nigeria will be based.

It remains for us on behalf of all the visitors to give our thanks to all

those who gave us hospitality: to Professor Fatunla and his team for

inviting us and for their hard work on our behalf; to the Vice Chancellor

of the university and his staff for their support to the conference; to the

Nigerian National Petroleum Corporation for accommodating us; and to the

many staff and students who welcomed us so warmly.

Endnote

=======

Fundamentals of Fortran Programming by Simeon Ola Fatunla, Ada Jane

Press, Benin City, Nigeria, Nov 1993, 460 pp, price 20 UK pounds or 30 US

dollars

Proceedings of Benin Conference 1988+1990 (combined), ed. Simeon Ola

Fatunla, University of Ibadan Press plc, Jan 1992, 308 pp, price 18 UK

pounds or 27 US dollars

Proceedings of Benin Conference 1992, ed. Smeon Ola Fatunla, Ada Jane

Press, Benin City, Nigeria, Jan 1994, 230pp, price 18 UK pounds or 27 US

dollars

These are availbale from Prof Fatunla, Head of Mathematics and Computer

Science, University of Benin, P.M.B. 1154, Benin City, Nigeria. Telex:

Nigeria (905)41365 UNIBEN NG

John Pryce

APPLIED & COMPUTATIONAL MATHS GROUP

RMCS SHRIVENHAM

SWINDON SN6 8LA, UK

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

From: SIAM <nelson@siam.org>

Date: Mon, 28 Feb 94 10:03:37 EST

**Subject: Contents, SIAM Optimization**

SIAM J. ON OPTIMIZATION 4-2 MAY 1994

Line Search Procedures for the Logarithmic Barrier Function

Walter Murray and Margaret H. Wright

Superlinearly Convergent O( nL)-Iteration Interior Point Algorithms

for Linear Programming and the Monotone Linear Complementarity

Problem

Kevin McShane

Convergence Properties of a Class of Rank-two Updates

Paul T. Boggs and Jon W. Tolle

Can Parallel Branch and Bound Without Communication be Effective?

Per S. Laursen

Convergence Theory of Nonlinear Newton)Krylov Algorithms

Peter N. Brown and Youcef Saad

On the Resolution of Linearly Constrained Convex Minimization

Problems

Ana Friedlander, Jose Mario Martinez, and Sandra A. Santos

On Optimization Problems with Variational Inequality Constraints

J. V. Outrata

Triangular Decomposition Methods for Solving Reducible Nonlinear

Systems of Equations

J. E. Dennis Jr., Jose Mario Martinez, and Xiaodong Zhang

Extension of Hoffman's Error Bound to Polynomial Systems

Xiao-Dong Luo and Zhi-Quan Luo

Globally Convergent Inexact Newton Methods

Stanley C. Eisenstat and Homer F. Walker

An Interior Point Column Generation Method for Linear Programming

Using Shifted Barriers

John E. Mitchell

Predictor-Corrector Methods for a Class of Linear Complementarity

Problems

Sanjay Mehrotra and Robert A. Stubbs

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

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

Date: Thu, 3 Mar 1994 07:07:22 -0600 (CST)

**Subject: Contents, Linear Algebra and its Applications**

Linear Algebra and its Applications

Contents Volume 199

Leon Jay Gleser (West Lafayette, Indiana), Michael D. Perlman

(Seattle, Washington), S. James Press (Riverside, California),

and Allan R. Sampson (Pittsburgh, Pennsylvania)

A Brief Biography and Appreciation of Ingram Olkin 1

T. Ando (Sapporo, Japan)

Majorizations and Inequalities in Matrix Theory 17

Y. L. Tong (Atlanta, Georgia)

Some Recent Developments on Majorization Inequalities in

Probability and Statistics 69

Karl Mosler (Hamburg, Germany)

Majorization in Economic Disparity Measures 91

James V. Bondar (Ottawa, Ontario, Canada)

Comments on and Complements to: Inequalities: Theory of Majorization

and Its Applications, by Albert W. Marshall and Ingram Olkin 115

Hector F. Miranda and Robert C. Thompson (Santa Barbara, California)

Group Majorization, the Convex Hulls of Sets of Matrices and

the Diagonal Element - Singular Value Inequalities 131

Khakim D. Ikramov (Waterloo, Ontario, Canada)

A Simple Proof of the Generalized Schur Inequality 143

Steen A. Andersson (Bloomington, Indiana) and Michael D. Perlman

(Seattle, Washington)

A Characterization of Matrix Groups That Act Transitively on

the Cone of Positive Definite Matrices 151

Markus Abt (Augsburg, Germany)

A Note on the Product Correlation Rule 171

Srinivasa R. Arikati and Uri N. Peled (Chicago, Illinois)

Degree Sequences and Majorization 179

Berthold Heiligers (Augsburg, Germany)

Totally Nonnegative Moment Matrices 213

J. Ferrer, Ma I. Garcia, and F. Puerta (Barcelona, Spain)

Differentiable Families of Subspaces 229

M*Ua Asuncion Beitia and Juan M. Gracia (Vitoria-Gasteiz, Spain)

Local Behavior of Sylvester Matrix Equations

Related to Block Similarity 253

R. B. Bapat and Subhash C. Kochar (New Delhi, India)

On Likelihood-Ratio Ordering of Order Statistics 281

B. Mond and J. E. Pecaric (Bundoora, Victoria, Australia)

Inequalities Involving Powers of Generalized Inverses 293

Jianming Miao and Adi Ben-Israel (New Brunswick, New Jersey)

On IP-Approximate Solutions of Linear Equations 305

S. W. Drury (Montreal, Quebec, Canada)

A Bound for the Determinant of Certain Hadamard Products

and for the Determinant of the Sum of Two Normal Matrices 329

Ingo Althofer (Bielefeld, Germany)

On Sparse Approximations to Randomized Strategies and

Convex Combinations 339

H. K. Wimmer (Wurzburg, Germany)

Roth's Theorems for Matrix Equations With Symmetry Constraints 357

M. Knott and C. S. Smith (London, England)

On a Generalization of Cyclic Monotonicity and Distances

Among Random Vectors 363

Alan Hoffman (Yorktown Heights, New York) and Uriel G. Rothblum

(Haifa, Israel)

A Proof of the Convexity of the Range of a Nonatomic Vector Measure

Using Linear Inequalities 373

Russell Merris (Hayward, California)

Degree Maximal Graphs Are Laplacian Integral 381

S. W. Drury (Montreal, Quebec, Canada)

On a Theorem of Wielandt and the Compounds of Unitary Matrices 391

Xiao-Li Meng (Chicago, Illinois) and Donald B. Rubin (Cambridge,

Massachusetts)

On the Global and Componentwise Rates of Convergence

of the EM Algorithm 413

Rafael Bru, Juana Cerdan, and Ana M. Urbano (Valencia, Spain)

An Algorithm for the Multiinput Pole Assignment Problem 427

Author Index 445

Special Issues in Progress

1. Special Issue Honoring Marvin Marcus; special editors are Bryan E. Cain,

Moshe Goldberg, Robert Grone, and Nicholas J. Higham. To appear as Volume 201,

April 1, 1994.

2. Linear Systems and Control, Third Special Issue; special editors are

A. C. Antoulas, P. A. Fuhrmann, M. L. J. Hautus, and Y. Yamamoto. Submission

deadline: November 30, 1992. To appear as Volumes 203/204/205, May/June/July

1, 1994.

3. Special Issue Honoring Chandler Davis; special editors are Rajendra

Bhatia, Shmuel Friedland, and Peter Rosenthal. Submission deadline: March 31,

1993. To appear as Volume 206, July 15, 1994.

4. Proceedings of the Third Conference of the International Linear Algebra

Society at Pensacola; special editors are Dianne P. O'Leary, Leiba Rodman, and

Helene Shapiro. Submission deadline: June 30, 1993. Details provided with the

conference announcement.

5. Proceedings of the conference ``Matrices and Graphs'' in honor of John

Maybee's 65th birthday, held at Boulder, Colorado, May 7, 8, 1993. Special

editors: C. R. Johnson and J. R. Lundgren. Submission deadline: August 31,

1993. Details provided with the conference announcement.

6. Fourth Special Issue on Linear Algebra and Statistics; special editors

are Jeffrey J. Hunter, Simo Puntanen, and George P. H. Styan. Submission

deadline: June 30, 1993. Details in Volume 177, December 1992.

7. Proceedings of the workshop ``Nonnegative Matrices, Applications and

Generalizations'' and the Eighth Haifa Matrix Theory conference held at Haifa,

Israel, May 31-June 4 and June 7-June 10, 1993, respectively. Special

editors: S. Friedland, D. Hershkowitz, and R. Loewy. Submission deadline:

September 15, 1993. Details provided with the conference announcement.

8. Special Issue Honoring Miroslav Fiedler and Vlastimil Ptak; special

editors are Wayne Barrett, Angelika Bunse-Gerstner, and Nicholas Young.

Submission deadline: August 31, 1993. Details in Volume 179.

9. Proceedings of the Fourth Conference of the International Linear

Algebra Society at Rotterdam; special editors are Harm Bart, Ludwig Elsner,

and Andre Ran. Submission deadline November 30, 1994. Details provided with

the conference announcement.

10. Special Issue Honoring J. J. Seidel: special editors are Aart Blokhuis,

Willem H. Haemers, and Alan J. Hoffman. Submission deadline: August 30, 1994.

Details in Volume 193, November 1, 1993.

Special issues are available to individuals at a reduced rate. For

further information, please contact Yusuf Guvenc, Journals Customer Service,

Elsevier Science Inc., 655 Avenue of the Americas, New York, NY

10010; Tel. 212-633-3955; Fax 212-633-3990.

Special Issues Vol. 199

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

End of NA Digest

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