**Today's Topics:**

- Last Call for SIAG/LA Prize
- Sparse Solvers for Overdetemrined Systems
- Block Tridiagonal Matrices
- Shampine/Gordon Integrator in C
- C Source for a Stiff ODE Integrator
- Three Measures of Precision in Floating Point Arithmetic
- Meeting on Mathematics, Computations, and Reactor Physics
- Second NIU Conference
- Position at the University of Auckland
- Postgraduate Opportunity at University of Durham
- Position at Centenary College of Louisiana
- Position at Lawrence Livermore Laboratory

From: Mike Heath <heath@csrd.uiuc.edu>

Date: Sun, 14 Apr 91 21:23:36 CDT

This is a reminder that the deadline is April 30 for nominations

of papers for the SIAG/LA Prize for the best paper in applicable

linear algebra for the years 1988-1990. Please see previous

announcements for details and eligibility rules. Nominations

should consist of a complete bibliographic citation and a brief

statement justifying the nomination, and should be directed to

the Prize Committee Chairman at the following address:

Michael T. Heath

Center for Supercomputing Research and Development

305 Talbot Laboratory

University of Illinois

104 South Wright Street

Urbana, IL 61801-2932

Phone: 217-244-6915

Fax: 217-244-1351

Email: heath@csrd.uiuc.edu

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

From: Rob MacLeod <macleod@vissgi.cvrti.utah.edu>

Date: Sun, 14 Apr 91 21:28:58 MDT

Hello na-netters,

I am looking for a solver that will work on a slightly overdetermined linear

system which is very sparse and reasonably large (ca. 3024 by 2832). It

arises from a minimization problem with which I can perform inteprolation

of electric potential values over a three-dimensional surface (the human

thorax). I matrix is not symmetric, or shouldn't be in theory, and I have

not yet checked diagonal dominance or positivity.

In the past, I have used direct QR-solvers on the full matrix in problems

of this type which were a bit smaller (1112 by 1048) in very tolerable

amounts of time (6 minutes) on an IBM RS/6000 520. Unfortunately, the

scaled-up version employing this approach for a 3024 by 2832 case ran for

12 hours before I gave up and stopped it. I need something considerably

faster that will run as a two-step process so that I can either

backsubstitute numerous right hand sides back into the decomposed matrix,

or do an iterative computation that will run in a few minutes.

Any suggestions out there?

Thanks,

Rob.

Rob MacLeod, Ph.D.

Nora Eccles Harrison Cardiovascular Research and Training Institute (CVRTI)

Building 500

University of Utah

Salt Lake City

Utah 84112

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

From: Tilak Ratnanather <sg391@city.ac.uk>

Date: Mon, 15 Apr 91 12:28:59 +0100

The following problem arising in magnetism was brought to

my attention by colleagues who'd greatly appreciate input

from experienced numerical analysts:

First question: is there a program that will compute the

eigenvalues of a BLOCK TRIDIAGONAL (Hermitian) MATRIX. Attempts

to search for one in netlib failed to yield a program. (Fortran

or even C is the preferred language).

Second question: at a more deeper level, the block tridiagonal

Hermitian matrix M may be written in the shorthand form:

(B*, A, B) where A and B are 5x5 matrices and * indicates the

complex conjugate and M is 100x100. Is there a way of reducing this

"large" problem to a sequence of reduced problems (or 5x5) problems?

One step that has been suggested is to make use of the diagonalised

form of A. The entries of A and B may be changed pending the physical

configurations.

Any ideas or pointers to references would be greatly appreciated. It

may be possible to summarise the responses at a later date.

Thanks a lot

Tilak Ratnanather

Dept of Mathematics

City University

Northampton Square

London EC1V 0HB

e-mail: sg391@city.ac.uk

jtr%mathsun1@city.ac.uk

na.ratnanather@na-net.ornl.gov

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

From: Roland England <R_ENGLAND@vax.acs.open.ac.uk>

Date: Tue, 16 APR 91 14:19:12 GMT

In connection with Kathryn Brenan's enquiry, we were also about to start

rewriting the Shampine/Gordon integration software (Adams numerical

integration code for ordinary differential equations) in C.

We would greatly welcome any available information, if this has already

been done elsewhere, and particularly, of course, if there is

a public domain version in existence which we could use.

Thanks for any replies.

Roland England

R_ENGLAND@vax.acs.open.ac.uk

NA.RENGLAND@na-net.ornl.gov

Tel. +44-908-65-2329

The Open University

Faculty of Mathematics

Milton Keynes

MK7 6AA

Great Britain

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

From: Steve Nichols <gt3930b@prism.gatech.edu>

Date: 20 Apr 91 13:57:35 GMT

I'm looking for C source code for a stiff ODE integrator. If anyone

has converted LSODE (from the netlib) to C, this would be perfect.

Thanks for any help,

Steve Nichols

Georgia Tech Physics Department

gt3930b@prism.gatech.edu

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

From: Nick Higham <mbbgsnh@cms.manchester-computing-centre.ac.uk>

Date: Sat Apr 13 14:31:37 PDT 1991

Three measures of precision in floating point arithmetic

by Nick Higham

This note is about three quantities that relate to the precision of

floating point arithmetic. For t-digit, rounded base b arithmetic the

quantities are

(1) machine epsilon (eps), defined as the distance from 1.0 to

the smallest floating point number bigger than 1.0 (and

given by eps = b**(1-t), which is the spacing of the

floating point numbers between 1.0 and b),

(2) mu = smallest floating point number x such that fl(1 + x) > 1, and

(3) unit roundoff u = b**(1-t)/2 (which is a bound for the relative

error in rounding a real number to floating point form).

The terminology I have used is not an accepted standard; for example,

the name machine epsilon is sometimes given to the quantity in (2).

My definition of unit roundoff is as in Golub and Van Loan's book

`Matrix Computations' [1] and is widely used. I chose the notation eps

in (1) because it conforms with MATLAB, in which the permanent

variable eps is the machine epsilon. [Ed. note: Well, not quite.

See my comments below. --Cleve]

The purpose of this note is to point out that it is not necessarily the

case that mu = eps, or that mu = u, as is sometimes claimed in the

literature, and that, moreover, the precise value of mu is difficult to

predict.

It is helpful to consider binary arithmetic with t = 3. Using binary

notation we have

1 + u = 1.00 + .001 = 1.001,

which is exactly half way between the adjacent floating point numbers

1.00 and 1.01. Thus fl(1 + u) = 1.01 if we round away from zero when

there is a tie, while fl(1 + u) = 1.00 if we round to an even last

digit on a tie. It follows that mu <= u with round away from zero (and

it is easy to see that mu = u), whereas mu > u for round to even.

I believe that round away from zero used to be the more common choice

in computer arithmetic, and this may explain why some authors define

or characterize u as in (2). However, the widely used IEEE standard

754 binary arithmetic uses round to even.

So far, then it is clear that the way in which ties are resolved

in rounding affects the value of mu. Let us now try to determine the

value of mu with round to even. A little thought may lead one to

suspect that mu <= u(1+eps). For in the b = 2, t = 3 case we have

x = u*(1+eps) = .001*(1+.01) = .00101

=> fl(1 + x) = fl( 1.00101 ) = 1.01,

assuming ``perfect rounding''. I reasoned this way, and decided to

check this putative value of mu in 386-MATLAB on my PC.

MATLAB uses IEEE standard 754 binary arithmetic, which has t = 53

(taking into account the implicit leading bit of 1). Here is what I

found:

>> format compact; format hex

>> x = 2^(-53)*(1+2^(-52)); y = [1+x 1 x]

y =

3ff0000000000000 3ff0000000000000 3ca0000000000001

>> x = 2^(-53)*(1+2^(-11)); y = [1+x 1 x]

y =

3ff0000000000000 3ff0000000000000 3ca0020000000000

>> x = 2^(-53)*(1+2^(-10)); y = [1+x 1 x]

y =

3ff0000000000001 3ff0000000000000 3ca0040000000000

Thus the guess is wrong, and it appears that mu = u*(1+2^(42)*eps)

in this environment! What is the explanation?

The answer is that we are seeing the effect of ``double-rounding'', a

phenomenon that I learned about from an article by Cleve Moler [2].

The Intel floating-point chips used on PCs implement internally the

optional extended precision arithmetic described in the IEEE standard,

with 64 bits in the mantissa [3]. What appears to be happening in the

example above is that `1+x' is first rounded to 64 bits; if

x = u*(1+2^(-i)) and i > 10 then the least significant bit is lost in

this rounding. The extended precision number is now rounded to 53 bit

precision; but when i > 10 there is a rounding tie (since we have

lost the original least significant bit) which is resolved to 1.0,

which has an even last bit.

The interesting fact, then, is that the value of mu can vary even

between machines that implement IEEE standard arithmetic.

Finally, I'd like to stress an important point that I learned from the

work of Vel Kahan: the relative error in addition and subtraction

is not necessarily bounded by u. Indeed on machines such as Crays

that lack a guard digit this relative error can be as large as 1. For

example, if b = 2 and t = 3, then subtracting from 1.0 the next

smaller floating number we have

Exactly: 1.00-

.111

-----

.001

Computed, without 1.00-

a guard digit: .11 The least significant bit is dropped.

-----

.01

The computed answer is too big by a factor 2 and so has relative

error 1! According to Vel Kahan, the example I have given mimics what

happens on a Cray X-MP or Y-MP, but the Cray 2 behaves differently and

produces the answer zero. Although the relative error in

addition/subtraction is not bounded by the unit roundoff u for

machines without a guard digit, it is nevertheless true that

fl(a + b) = a(1+e) + b(1+f),

where e and f are bounded in magnitude by u.

[1] G. H. Golub and C. F. Van Loan, Matrix Computations, Second Edition,

Johns Hopkins Press, Baltimore, 1989.

[2] C. B. Moler, Technical note: Double-rounding and implications for

numeric computations, The MathWorks Newsletter, Vol 4, No. 1 (1990), p. 6.

[3] R. Startz, 8087/80287/80387 for the IBM PC & Compatibles, Third

Edition, Brady, New York, 1988.

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

Editor's addendum:

I agree with everything Nick has to say, and have a few more comments.

MATLAB on a PC has IEEE floating point with extended precision implemented

in an Intel chip. The C compiler generates code with double rounding.

MATLAB on a Sun Sparc also has IEEE floating point with extended precision,

but it is implemented in a Sparc chip. The C compiler generates code

which avoids double rounding.

On both the PC and the Sparc

eps = 2^(-52) = 3cb0000000000000 = 2.220446049250313e-16

However, on the PC

mu = 2^(-53)*(1+2^(-10)) = 3ca0040000000000 = 1.111307226797642e-16

While on the Sparc

mu = 2^(-53)*(1+2^(-52)) = 3ca0000000000001 = 1.110223024625157e-16

Note that mu is not 2 raised to a negative integer power.

MATLAB on a VAX usually uses "D" floating point (there is also a "G"

version under VMS). Compared to IEEE floating point, the D format has

3 more bits in the fraction and 3 less bits in the exponent. So

eps should be 2^(-55), but MATLAB says eps is 2^(-56). It is actually

using the 1+x > 1 trick to compute what we're now calling mu. There

is no extended precision or double rounding and ties between two floating

point values are chopped, so we can find mu by just trying powers of 2.

On the VAX with D float

eps = 2^(-55) = 2.775557561562891e-17

mu = 2^(-56) = 1.387778780781446e-17

The definition of "eps" as the distance from 1.0 to the next floating

point number is a purely "geometric" quantity depending only on the

structure of the floating point numbers. The point Nick is making is

that the more common definition of what we here call mu involves a

comparison between 1.0 + x and 1.0 and subtle rounding properties of

floating point addition. I now much prefer the simple geometric

definition, even I've been as responsible as anybody for the popularity

of the definition involving addition.

-- Cleve

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

From: Milo Dorr <dorr@hyperion.llnl.gov>

Date: Sun, 14 Apr 91 15:34:53 PDT

The American Nuclear Society (Mathematics & Computation Division and

Reactor Physics Division) International Topical Meeting:

ADVANCES IN MATHEMATICS, COMPUTATIONS, AND REACTOR PHYSICS

April 28 - May 2, 1991

Green Tree Marriott

Pittsburgh, PA

The banquet speaker on Wednesday, May 1 will be George E. Lindamood of

the Gartner Group. The title of his lecture will be "Why

Supercomputing Matters: A Perspective of the Proposed Federal High

Performance Computing and Communication Program".

There will also be a plenary session at 9:30am on Monday, April 29,

consisting of a panel discussion on the topic "Perspectives on

Advances in Supercomputing Performance" moderated by James. R.

Kasdorf from Westinghouse Corporate Computer Services and the

Pittsburgh Supercomputing Center. The panelists and the titles of

their prepared presentations are:

Gregory J. McRae (Carnegie Mellon University)

"Grand Challenges in Computational Science"

W. B. Barker (BBN Advanced Computers, Inc.)

"Parallel Computing: Past, Present, and Future"

M. L. Barton (Intel Supercomputing Systems Division)

"Technology Development for Supercomputing 2000"

Kenichi Miura (Fujitsu America, Inc.)

"Perspectives on Advances in Supercomputer Performance

- Fujitsu's View"

Steve Nelson (Cray Research, Inc.)

"Heterogeneous Supercomputing: Now and Then"

For a copy of the Technical Program or further information, please

contact the Program Chairman:

I. K. Abu-Shumays

RT-Mathematics, 34F

Bettis Atomic Power Laboratory

P. O. Box 79

West Mifflin, PA 15122-0079

(412) 476-6469, FAX (412) 476-5151

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

From: Biswa Datta <dattab@math.niu.edu.

Date: Mon, 15 Apr 91 22:40:59 CDT

Second NIU Conference on Linear Algebra, Numerical Linear,

Algebra and Applications

May 3 - 5, 1991

Holmes Student Center

Northern Illinois University

Organizer and Chairman - Biswa Datta, Northern Illinois University

Advisor: Hans Schneider, University of Wisconsin - Madison

Sponsored By

The Institute for Mathematics and Its Applications (Minnesota)

and International Linear Algebra Society (ILAS)

Northern Illinois University

The purpose of the conference is to bring together researchers in linear

algebra, numerical linear algebra, and those working in various application

areas for an effective exchange of ideas and discussion of recent

developments and future directions of research.

All events will take place at the Holmes Student Center, Northern Illinois

University. Registration with begin at 7pm on Thursday, May 2. The

meeting itself with be Friday, May 3, through Sunday May 5.

Invited speakers include:

R. Thompson, University of California-Santa Barbara

R. Plemmons, Wake Forest University

Clyde Martin, Texas Tech University

Roger Horn, The Johns Hopkins University

Charles R. Johnson, College of William and Mary

Daniel Hershkowitz, Tecnion-Israel Institute of Technology

Robert Grossman, University of Illinois at Chicago

James R. Bunch, University of California-San Diego

Floyd Hanson, University of Illinois at Chicago

Chris Bischof, Argonne National Laboratory

William Gragg, Naval Post Graduate School at Monterey, California

Lothar Reichel, Naval Postgraduate School

Richard Brualdi, University of Wisconsin - Madison

Thomas Laffey, University College, Dublin, Ireland

Jose Dias de Silva, University of Lisbon, Lisbon, Portugal

S. Campbell, North Carolina State University

Kenneth Clark, Army Research Office

William Hager, University of Florida

George Cybenko, University of Illinois at Urbana-Champaign

Patricia Eberlein, University of Buffalo/SUNY

Kermit Sigmon, University of Florida

Daniel Boley, University of Minnesota

Homer Walker, Utah State University

Roland Freund, RIACS, NASA AMES Research Center

A. Yeremin, USSR Academy of Sciences

David Young, University of Texas, Austin

Michael Neumann, University of Connecticut

Avi Berman, Technion-Israel Institute of Technology

Chris Byrnes, Washington University

S. P. Bhattacharyya, Texas A & M University

Bijoy Ghosh, Washington University

Rama K. Yedavalli, Ohio State University

S. Friedland University of Illinois at Chicago

S. Wright, Argonne National Laboratory

Pradip Misra, Wright State University

Mohsen Pouramdi, Northern Illinois University

For more information about the program, contact faculty coordinator Biswa

Nath Datta, Department of Mathematical Sciences, at (815) 753-6759. For more

information about the logistics, contact Margaret Shaw, College of

Continuing Education, at (815) 753-1458.

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

From: J. C. Butcher <butcher@mat.aukuni.ac.nz>

Date: Wed, 17 Apr 91 10:13:28 NZS

THE UNIVERSITY OF AUCKLAND, NEW ZEALAND

LECTURESHIP

Applied and Computational Mathematics Unit

The University of Auckland invites applications for a lectureship

in the Applied and Computational Mathematics Unit within the

Department of Mathematics and Statistics. Applicants should have

a proven record in teaching and research in some branch of

Applied or Computational Mathematics. Applications from

candidates with expertise in a field that will strengthen and

enhance the existing research interests of the Applied and

Computational Mathematics Unit in differential equations and

their numerical solutions and applications of scientific computing

to physical and other problems are particularly welcome.

The University of Auckland has a student population of about

17,000 and is the only university in Auckland, a city with about

one million inhabitants. Mathematics and Statistics is the largest

department.

University positions are organised in a system similar to that of

the UK. Thus a lectureship is intended to be a permanent

appointment although, in the first instance, it is for a four year

term. Most appointments are continued after that period.

The salary scale for a lecturer begins at $NZ37,440 and increases

in annual increments. (Details of the salary scale and prospects

for promotion are available on request).

It is hoped that the successful applicant will take up his or her

duties by 1 August 1991 or soon after.

Applications, in accordance with the "Method of Application"

(available on request) should be submitted as soon as possible and

no later than 30 June 1991.

The University of Auckland is an Equal Opportunity Employer

For further information or enquiries about the position please

contact the Head of the Applied and Computational Mathematics Unit

Professor J. C. Butcher using email.

butcher@mat.aukuni.ac.nz or na.butcher@na-net.ornl.gov

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

From: Alan Craig <Alan.Craig@durham.ac.uk>

Date: Thu, 18 Apr 91 16:35:46 BST

The Department of Mathematical Sciences, University of Durham and the British

Gas Research Station in Northumberland have a CASE studentship in

Adaptive Finite Element Analysis

for Nonlinear Elastic Problems

The award is for three years, tenable from October 1991 and for a programme of

research leading to a PhD.

Outline of project: the finite element method is the computational tool for the

solution of structural analysis problems. The technique relies on replacing the

underlying differential equations by an approximating set of equations. However

the correct choice of this approximating set is by no means a trivial procedure.

In recent years adaptive methods have been developed which attempt to choose the

approximation in an automatic way linked to the problem. The analysis and

implementation of these methods for linear problems is now well understood. The

situation for nonlinear systems is however, less satisfactory and the interest

in adaptive techniques for general nonlinear response stems from the need to

maintain structural integrity in hazardous situations. In particular British

Gas are interested in techniques which can be used to analyse their offshore

rigs.

The project will maintain a careful balance between theoretical analysis and

practical implementation. Experience has shown that in this area, as in many

others, the implementation can be guided and enriched by the analysis. The

ultimate aim is to produce high quality algorithms for nonlinear problems.

As part of the project the successful applicant will work in the British Gas

Research Station for periods totaling three months under the supervision of the

Industrial Supervisor Mrs. Jane Haswell.

The applicant will have, or will be about to obtain, a good honours degree in

Mathematics, Engineering or a related discipline. In addition to the standard

SERC award British Gas will make an extra payment of 1620 pounds per annum to

the student.

Further information can be obtained from Dr. Alan Craig at the address below and

informal enquiries are welcomed. Application should be made to the same address

and should include the names and addresses of at least two referees, one of whom

should be able to judge the applicants suitability for research.

Dr.A.W.Craig

Department of Mathematical Sciences

University of Durham

South Road

Durham DH1 3LE

England

na.craig@na-net.ornl.gov

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

From: Antonio Pizarro

Date: Fri, 19 Apr 91 08:35:56 IST

Applications are invited for two tenure-track positions in MATH. A

Ph.D in Mathematics is required. Linear Algebra, Topology or Applied

Math are preferred fields, but all fields are considered. Beginning

Fall 1991. Send resume and three letters of recommendation to:

Antonio G. Pizarro, Chair

Math Department

Centenary College of Louisiana

Shreveport LA 71134, USA.

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

From: Anthony Skjellum <tony@helios.llnl.gov>

Date: Fri, 19 Apr 91 11:15:54 PDT

Postdoctoral Position in Parallel Computation - Lawrence Livermore

A postdoctoral position in scientific parallel algorithms research is

presently available in the Numerical Mathematics Group (NMG) at the

Lawrence Livermore National Laboratory, Computing and Mathematics

Researh Division. Candidates should be well versed in parallel

computation; particularly, distributed memory machines and issues.

Experience with large-scale parallel scientific algorithms and

applications is strongly desired. In-depth experience with the Unix

operating system and the C/C++ languages is also desired. Candidate

will participate in the growing NMG research effort in parallel

computation, but also will enjoy freedom to explore his or her own

allied research interests. A one year position is offered, renewable

for a second year if both NMG and the fellow concur. Candidate should

have completed his or her Ph.D. in an appropriate discipline prior to

October 1, 1991. Starting date is on or after October 1, 1991. US

citizenship is required. Send three letters of recommendation, resume,

and publications list to Dr. Anthony Skjellum, LLNL L-316, PO Box 808,

Livermore, CA 94550. (415)422-1161. e-mail: tony@helios.llnl.gov.

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

End of NA Digest

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From surfer.EPM.ORNL.GOV!nacomb Sat Apr 27 22:36:25 0400 1991