NA Digest Sunday, December 11, 1994 Volume 94 : Issue 50

Today's Editor:
Cleve Moler
The MathWorks, Inc.

Submissions for NA Digest:

Mail to

Information about NA-NET:

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From: Leslie Greengard <>
Date: Thu, 8 Dec 94 11:43:31 -0500
Subject: Greengard Method

A message on the NA-NET last week referred to "the Greengard method"
and asked for a reference. The algorithm being referred to is
most likely the fast multipole method (FMM). It was initiated
in work by V. Rokhlin

V. Rokhlin (1985), Rapid solution of integral equations of classical
potential theory, J. Comput. Phys. 60, pp. 187-207,

and generalized in a series of subsequent papers

L. Greengard and V. Rokhlin (1987),
A fast algorithm for particle simulations,
J. Comput. Phys. 73, pp. 325-348.

J. Carrier, L. Greengard, and V. Rokhlin (1988),
A fast adaptive multipole algorithm for particle simulations,
SIAM J. Sci. Statist. Comput. 9, pp. 669-686.

L. Greengard and V. Rokhlin (1988),
Rapid Evaluation of Potential Fields in Three Dimensions,
in Vortex Methods, C. Anderson and C. Greengard (eds.),
Lecture Notes in Mathematics, vol. 1360,
Springer-Verlag, pp. 121-141.

The work described in these papers is also available in book form:

L. Greengard (1988),
The Rapid Evaluation of Potential Fields in Particle Systems,
MIT Press, Cambridge.

Because many people seem to have learned of the FMM from the last source,
it is occasionally referred to as "the Greengard method." It should
not be. On the book jacket, the name "Rokhlin-Greengard" algorithm
is used, but "fast multipole method" is both more descriptive and
more common usage.

Leslie Greengard


From: Alan Edelman <>
Date: Tue, 6 Dec 94 13:42:11 EST
Subject: Random Arithmetic and x*(1/x)

In discussing the Pentium FDIV bug Cleve Moler wrote:

>> There are serious and subtle numerical difficulties associated
>> with using even a correct multiply and subtract to decide if a
>> proposed quotient is correct. For example, simply replacing
>> N/D by N*(1/D) won't work if you after the correctly rounded,
>> IEEE floating point result.

For a fun brief education on such subtle issues, I whipped up a little
note on when x*(1/x)=1 which may be clicked on from

On my own personal wishlist is that every theory of computation
student would hear one lecture on the IEEE standard for floating
point computation. Better yet he or she should be obliged to
take a numerical analysis course.

And, on the same subject, Manny Blum wrote

>> We must demand radically stronger standards of reliability.
>> But how is such reliability to be achieved? We believe that the
>> answer is via run-time result-checking and self-correcting. In
>> particular, we believe that the chip of the future will have efficient
>> checkers and correctors embedded in its hardware. For example, every
>> time a chip divides, it will do a multiplication to check the answer,
>> and, if the answer is incorrect, will call a randomized self-corrector
>> such as the one described above. Note that testing the chip's
>> division before release will then be a simple matter: all the company
>> need do is run the chip on a number of random inputs and verify the
>> correctness of each answer. It is thus assured that the chip can only
>> be incorrect on at most a small portion of all possible inputs; and a
>> randomized self-corrector will be capable of entirely suppressing such
>> occasional bad cases.

To follow Einstein, I don't like playing dice with arithmetic. (Yes,
I know Einstein was wrong on the "dice" issue.) My fear would be that
we would be lulled into producing sloppy arithmetic because we expect
the randomizer to fix it for us. Given that correct arithmetic is
achievable by careful human beings, I am not in favor of bogging down
chips with randomized error fixers. Some things are worth just getting


From: Vaughan Pratt <pratt@Sunburn.Stanford.EDU>
Date: 4 Dec 1994 07:56:12 GMT
Subject: The Bad Scenario for FDIV--Simplified Account

In article <>, Tim Arheit
<> wrote:

>The problem is that my software doesn't use random number as data. One
>of the postes in this group shows that simple division of ~integer numbers
>shows a significant error (something on the order of 100 times less accurate)
>4.99999999/14.999999 (5/15) (I think these are some of the example
>numbers given, it's in this group somewhere) generated significant error.
>The point is that integer constants in a floating point equation are far
>from random.

Let me correct a minor detail and at the same time repackage what I
said in two earlier messages in a hopefully more digestible and
memorizable form.

The exact example here subtracted one millionth (easy to remember) from
each of 5 and 15, i.e. 4.999999/14.999999. The correct value is
0.33333329, Pentium math makes it 0.333329, wrong in the fifth decimal
place, specifically a relative error of 1.2 in 10^5.

Other such rationals are 7/48 and 9/54. For each of these, if you
subtract one millionth from both numerator and denominator before
dividing, you again obtain a relative error of about one in a hundred

Among rationals with numerator and denominator both bounded by 1000,
each decremented by a millionth, there are 14 that behave as badly as
the three examples above, and an additional 412 that the Pentium
evaluates with a relative error between 10^-5 and 10^-7. (For
comparison, using single precision instead of double yields a maximum
relative error of 6*10^-8, so all these errors are worse than would
result merely from using single precision instead of double.)

Hence if you compute with randomly chosen approximate (in the above
sense) rationals from that population, the probability of an error in
the fifth place is one in 70,000, while the probability of an error in
the sixth or seventh place is one in 2,000.

The P90 can do better than two divisions per microsecond, at which
rate, assuming the above population of approximate rationals, the small
error (sixth or seventh place) occurs once a millisecond on average
while the large error (fifth place) occurs once every 35 milliseconds.

When the division operands are bounded by 100 instead of 1000, the
1/2,000 figure for the small error drops to 1/200 (a factor of 10
worse) while the 1/70,000 rate for the large error drops to 1/2,000 (a
factor of 35 worse), i.e. the large errors now happen once a

Detailed tables of such errors, along with a program for verifying my
conclusions for yourself, can be found in my two earlier messages on
this subject on comp.arch, Search for the phrase
"ibruis" (a variable in my program) or the subject "A natural scenario
with high FDIV bug probability (was: In Intel's Defense...)".

Vaughan Pratt


From: Hassane Sadok <>
Date: Tue, 6 Dec 1994 14:08:38 --100
Subject: Sparse Matrix Times a Packed Vector

Dear Colleagues,
I would like to know what is the best way for implementing in Fortran
a product of a sparse matrix stored in compressed sparse row (CSR) format by
a packed vector.
Is the best way, the one achieved by first expanding the packed vector into a full-lenght vector?
Many thanks for your help.

Hassane SADOK
Laboratoire d Analyse Numerique et d Optimisation
Universite des Sciences et Technologies de Lille.
Bat M3. 59655 Villeneuve d Ascq cedex.


From: George Miminis <>
Date: Tue, 6 Dec 1994 19:42:51 -0330
Subject: Despertly Seeking Matrices

Has anybody encountered the following class of (2^k)x(2^k) matrices, (for
some natural number k), defined recursively as follows:

(i): If k=1 then

(a -b)
(b a)

is such a matrix.

(ii): If A, B are such matrices of size 2^k each, then

(A -B)
(B A)

is such a matrix of size 2^(k+1).

It is well known that complex numbers are defined as 2x2 such matrices. As
an example of (2^3)x(2^3) such matrix consider

                         ( 1|-2|-3  4|-5  6  7 -8)
(--|--| | )
( 2| 1|-4 -3|-6 -5 8 7)
(--|--|-----| )
( 3|-4| 1 -2|-7 8 -5 6)
(--|--| | )
( 4| 3| 2 1|-8 -7 -6 -5)
( 5|-6|-7 8| 1 -2 -3 4)
(--|--| | )
( 6| 5|-8 -7| 2 1 -4 -3)
(--|--|-----| )
( 7|-8| 5 -6| 3 -4 1 -2)
(--|--| | )
( 8| 7| 6 5| 4 3 2 1)

Please note that the above matrices are also defined by their first column.
The process with which they can be generated by their first column is rather
obvious by the above matrix and the partitioning.

If anybody has any information associated with the above matrices I would
appreciate it if she/he let me know.

George Miminis
Dept. of Computer Science
Memorial University of Newfoundland
St. John's, NF, CANADA
A1C 5S7


From: Bart Motmans <>
Date: Tue, 6 Dec 1994 13:12:28 +0100
Subject: Reminder of Deadline for Benelux Meeting

Reminder :

December 15, 1994 : Deadline for submitting proposals for Special
Sessions and 1-page abstracts for short lectures for the
'14th Benelux Meeting on Systems and Control', which is
from March 29-31, 1995 in Houthalen, Belgium.

Proposals/abstracts should be sent to :

Bart Motmans
ESAT - Department Electrical Engineering
Katholieke Universiteit Leuven
Kardinaal Mercierlaan 94
B-3001 Leuven
Tel.:32/16/22.09.31 (after 1/1/95 : 32/16/32.11.11)
Fax.:32/16/22.18.55 (after 1/1/95 : 32/16/32.19.86)
email :


From: Roger G Ghanem <>
Date: Tue, 6 Dec 1994 13:13:45 -0500
Subject: Conference on Computer Methods in Water Resources


The International Conference on Computer Methods and Water Resources
aims at bringing together engineers and scientists with a common
interest in applying computational methods for the solution of
practical problems related to surface and sub-surface fluid
flow. The Conference's themes will encompasses conceptual,
physical and mathematical modeling, numerical techniques, engineering
applications, and software development. Papers are invited on the
topics indicated below and others falling within the scope of the Conference.

Three copies of each abstract of no more than 300 words, clearly stating
the purpose, results and conclusion of the work to be described in the final
paper should be submitted to the Conference Secretariat as soon as possible.
Each abstract should include key words and related conference topics.
Authors will be notified before March 15, 1995.


Ground Water Flow Models Shallow Water Models
Pollution Transport and Dispersion Flow in Rivers and Channels
Wave Propagation Coastal Engineering Models
Estuarine Problems Reservoir Modelling
Sedimentation Multiphase Flow
Hydrological Studies Flow in Fractured Porous Media
Porosity Modelling GIS Applications and Surveying Techniques
Uncertainty Modelling Satlwater Intrusion Problems
Water Management Mathematical and Physical Modelling
Experimental and Laboratory Work Water Resources Management


Professor Y. Abousleiman
School of Petroleum and Geological Engineering
Energy Center
University of Oklahoma
Norman, OK 73019
Tel: +1 405 325 2901 Ext 146 Fax: +1 405 325 7511

see also:


From: Gene Golub <golub@sccm.Stanford.EDU>
Date: Tue, 6 Dec 94 21:55:38 PST
Subject: Scientific Computation and Differential Equations


SciCADE 95
International Conference on
Scientific Computation and Differential Equations
Stanford, California, March 28--April 1, 1995


This meeting will feature current research in scientific computing with
an emphasis on the numerical solution of differential equations which
arise in science and engineering, particularly ordinary differential
equations. The meeting will close with a celebration of the sixtieth
birthday of C. William Gear.

Plenary speakers include:

W. Beyn S. Campbell P. Deuflhard L. Dieci S.S. Filippov
C.W. Gear C. Grebogi E. Hairer C. Johnson W. Kahan
C. Lubich T. Mitsui E. Platen A. Sameh
J.M. Sanz-Serna T. Schlick L.F. Shampine P. Shirkov
A. Toomre J. White S. Wright

Minisymposia (and their organizers) include:

Boundary Value Problems (U. Ascher)
ODEs in Chemical and Atmospheric Sciences (Z. Zlatev)
Computer-Aided Tools for Handling ODEs (M. Bronstein)
Computing Invariant Sets (I. Kevrekidis)
Delay Differential Equations (A. Iserles)
Differential-Algebraic Equations I (S. Campbell)
Differential-Algebraic Equations II (R. Maerz)
Educational Issues (K. Stewart)
Hamiltonian Systems (J. Sanz-Serna)
Linear Algebra Issues (P. Saylor)
Long-time Integration (D. Stoffer)
Multibody Dynamics (K. Clark)
Numerical Methods for Stochastic Differential Equations (E. Platen)
ODE methods in PDEs (R. Russell)
ODE Software (A. Hindmarsh)
Parameter Estimation and Design Optimization (S. Wright)
Practical Parallel Methods (K. Burrage)
Shadowing (H. Kocak)
Sinc Methods for ODEs and PDEs (F. Stenger)
Trajectory Control (K. Brenan)
Validated Computation of Solutions of ODEs (H. Stetter)
Waveform Relaxation (J. White)

Organizing Committee:

Gene Golub (Stanford University)
Linda Petzold (University of Minnesota)
Robert Skeel (University of Illinois at Urbana-Champaign)
Andrew Stuart (Stanford University)

To obtain further details and registration information
send an e-mail message to:


From: IMACS Administration <>
Date: Thu, 8 Dec 94 15:17:15 EST
Subject: Symposium on Systems Analysis and Simulation

5th. IMACS International Symposium on Systems Analysis and Simulation -

Technical University Berlin, Germany
June 26-30, 1995

In the last decade the computer simulation became a key technology in
industry, economics and natural sciences. The request to manage and
control difficult processes has forced the development of very complex
dynamic systems and extended simulation tools. Now the increasing
availability of parallel computer systems offers a new dimension for
real time simulation of such complex dynamic systems. Beside papers
that deal with aspects of parallel processing, advanced tools and
applications in important fields of systems analysis and simulation
are of particular interest.

TOPICS include: Computational and Mathematical Aspects of High
Performance Scientific Computing (HPSC) and Parallel Applications;
Analysis of Complex dynamic and Nonlinear Systems; Challenges and
Applications in Industry, Natural Science, Economics, Medicine,
Informatics, Engineering and Environment.

Submission of Abstracts (3 copies, 1-2 pages) before: December 15, 1994
Notification of Acceptance: February 1, 1995
Camera-ready Papers (2 copies, 4-6 pages) due: April 1, 1995

PUBLICATIONS: All invited and accepted papers will be published in the
conference proceedings. Additionally, selected and extended papers
will be published in the IMACS journal MATHEMATICS AND COMPUTERS IN

For further information contact:

Secretariat SAS'95
Rudower Chaussee 5, Geb. 13.7
D-12489 Berlin - Germany
Tel: 49 30 6392 1814/1800 / Fax: 49 30 6392 1805


From: I J Anderson <>
Date: Fri, 9 Dec 94 12:15:56 GMT
Subject: Short Course in Numerical Computing with MATLAB


One-week Short Course for Industry. January 23-27, 1995.
School of Computing and Mathematics, University of Huddersfield.

This course provides a sound introduction to the methods and
principles of numerical mathematics by computer, based on the
use of the popular package MATLAB
There will be ample opportunities
for hands-on experience in solving problems by computer.

The course is intended for those who have a reasonable background in
mathematics and/or scientific computing, and who wish to gain
confidence and experience in the use of computers to solve standard

Topics covered will include:
Numerical methods and analysis - requirements, principles
MATLAB - introduction, features and use.
Use of MATLAB in numerical mathematical methods -
Calculus, Nonlinear Equations, Matrices, Data Fitting,
Differential Equations.

The course will be directed by Professor John Mason, Head of Maths
and Stats Division at Huddersfield, who is an international expert
in this field ( author of 3 basic texts and Editor-in-Chief of the
journal Advances in Computational Mathematics). Several experienced
staff of the School of Computing and Maths will be lecturing and
supervising computer practical sessions.
The School's Sun workstation network will be used for practicals.

MSc Programme
This course is part of the University's modular MSc programme

For bookings and further information about the course or the MSc,
please contact :
Susan Forrester,
School of Computing and Maths,
University of Huddersfield,
Telephone: 01484-472049


From: Mike Meyer <>
Date: Fri, 09 Dec 1994 10:33:39 -0500
Subject: Interface 95 Announcement

Interface '95

27th Symposium on the Interface
Computing Science and Statistics
June 21--24, 1995
Convention Center and Vista Hotel---Pittsburgh PA.

The Interface Conference is the premier annual conference on the interface of
computing and statistics. It is sponsored by the non-profit Interface
Foundation of North America, and will be hosted in 1995 by Carnegie
Mellon University and the Pennsylvania State University with Michael
Meyer and James Rosenberger as joint program chairs.
The 1995 conference will be in Pittsburgh Pennsylvania, home of
many excellent academic and industrial statistics and computer science
research programs, and one of America's most livable cities.


The Symposium is being organized around the theme of ``Statistics and
Manufacturing,'' with a sub-theme of green manufacturing, the
environment, and quantitative environmental science.

The keynote speaker will be Raj Reddy, Dean of the School of Computer
Science at Carnegie Mellon and the most recent receipient of the A.M.
Turing award.

Call for Papers:

Sessions will include invited and contributed papers. Authors who
wish to give a contributed paper should submit two copies of an
abstract by February 28, 1995. The abstract should not exceed
one-half page (text=6.5 inches wide by 4 inches tall) with centered
title, author(s), and address. Invited and contributed papers are to
be submitted for the proceedings by July 15, 1995. Proceedings
submissions must be camera ready.



The registration fee is \$155 for members of the cooperating
societies, ASA, IMS, SIAM, ORSA, the Biometrics Society (ENAR and
WNAR) and for persons affiliated with Penn State University and
Carnegie-Mellon University. For others the fee is \$175. The
registration fee covers the reception, coffee breaks, banquet, and


Conference registration begins on Wednesday afternoon (June 21). The
first official conference event is a Wednesday evening mixer.
Technical sessions will be held on Thursday and Friday from 8:15
a.m.--5:15 p.m. and from 8:15 a.m. to noon on Saturday. Breaks are
scheduled between the sessions and also for lunch. All conference
meetings will be held in the David L. Lawrence Convention Center,
which is linked to the hotel by an enclosed walkway.


For further registration and hotel information, contact
Phone: (412) 268-3108 Facsimile: (412) 268-7828
Mail: Interface95, Department of Statistics, Carnegie Mellon University,
5000 Forbes Avenue, Pittsburgh, PA 15213, USA.

Further Information:

For current information, use the World Wide Web to access the URL

Mike Meyer, Computing Services and Department of Statistics,
Carnegie Mellon University


From: Andy Wathen <>
Date: Fri, 9 Dec 94 16:35:55 GMT
Subject: Bristol-Bath Numerical Analysis Day

The next


will be held in Lecture Theatre SM2, School of Mathematics,
University Walk, Bristol, UK on Monday 9th January 1995.

All are invited to attend this informal (and free!) set of
talks on current research to be given by local speakers:
Yves Tourigny, David Worth, Tony Humphries,
Alastair Spence, Adrian Hill, Andy Wathen
and our `guest' speaker, Professor Ernst Stephan of
the University of Hannover.

The talks will start at 10:45 preceded by coffee (from 10:15),
and will end at 16:05.

For full programme contact:
Andy Wathen (+44 0117 928 7995)


From: A. Spence <>
Date: Fri, 9 Dec 94 18:18:06 GMT
Subject: Positions at Bath University



Readerships/Lectureships in Mathematics

The School of Mathematical Sciences is comprised of three Groups:
Mathematics, Statistics and Computer Science.

Applications are now sought for two vacancies in the Mathematics Group
and appropriately qualified candidates may be appointed to
Readerships. It is hoped that one appointment will be made in each of
Pure Mathematics and Applied Mathematics. The appointments are tenable from
1st September 1995.

Appointments will be made of candidates with excellent research records
or excellent potential for research in areas related to the following:
Solid Mechanics, Mathematical Biology, Control Theory, Numerical
Analysis, Dynamical Systems, Differential Equations, Analysis,
Geometry, Calculus of Variations. Further particulars are available
by anonymous ftp from

or can be found using WWW at


For further information, contact the Head of School, Professor A.
Spence, (Tel: +44 1225 826011, Fax: +44 1225 826492, e-mail or or the
Director of Personnel, Mr P J Hill (Tel:+44 1225 826702,
Fax:+44 1225 826559). The closing date for applications is: 23rd January 1995.


From: Warren Nichols <nichols@GAUSS.MATH.FSU.EDU>
Date: Fri, 9 Dec 94 13:34:50 -0500
Subject: Positions at Florida State University

Symbolic Computation

The Department of Mathematics plans to focus its hiring over the next
several years on Computational Mathematics: Symbolic and Numeric
Computation. We expect to add three faculty members in each of Symbolic
and Numeric Computation within the next three years. We are now
inviting applications for a senior position in Symbolic Computation, to
begin in Fall 1995.

The successful candidate will be expected to take a leadership role in
developing and shaping the Symbolic Computation program. As well as an
outstanding research record, excellence in teaching is essential. There
should be evidence that the candidate will be effective in working with
the university administration and with funding agencies. Favorable
consideration will be given to the potential for interaction with
mathematics faculty members, with the Supercomputer Computations
Research Institute, and with the Department of Computer Science.

Complete applications should include a detailed curriculum vitae and
the names of three references. Applications received by February 17, 1995
will receive full consideration. Address all communications to: Warren
Nichols, chair, Search Committee, Department of Mathematics, Florida
State University, Tallahassee FL 32306-3027 (

Florida State University is an EEO/AA employer, and especially
encourages applications from women and minorities.


From: Julia Addy <>
Date: Wed, 7 Dec 1994 09:09:10 -0500
Subject: Position at Cornell Theory Center

CORNELL THEORY CENTER - Position Opening for an Education and
Training Consultant

The Cornell Theory Center is one of four national supercomputing centers
established by the National Science Foundation. The Center is a
leading-edge computational science laboratory that provides scalable,
parallel computing resources to the national research community. The
Center's environment includes the largest IBM SP2 supercomputer
configuration in the world.

We are seeking a highly motivated individual with a strong scientific and
technical background to fill the position of Education and Training
Consultant. The individual in this position will provide a full range of
education and training programs on parallel computing environments.
Responsibilities include developing and implementing educational workshops,
preparing technical documentation and lecture materials, developing on-line
tutorials, and evaluating and developing new tools and techniques for
educational programs.

Requirements: BS in science or engineering, MS preferred. Minimum 2-3
years experience in a scientific computing environment. Relevant
experience in education and development of technical training materials.
Programming in FORTRAN or C and solid experience with UNIX required.
Parallel programming experience a plus.

Interested applicants should forward a cover letter and resume to:
Julie Addy
Cornell Theory Center
Dept. NA
Cornell University
Ithaca, NY 14853-3801

Cover letters and resumes may be submitted on-line in ASCII or postscript forms



From: Grace Liberato <>
Date: 7 Dec 1994 15:58:42 -0700
Subject: Position at Colorado State University


Ph.D. and potential for excellence in teaching and research required.
Specialization in applications of mathematics preferred. Salary is
commensurate with qualifications. The successful applicant will be
expected to conduct a vigorous program of research; pursue external
funding; teach an average of 6 credit hours per semester; direct
degree programs. (This position is contingent upon the availability of
funds.) Send resume and three letters of recommendation to:
R.E. Gaines, Department Head
Colorado State University
Department of Mathematics
121 Engineering
Fort Collins, CO 80523
Deadline: February 1, 1995
Colorado State University is an EEO/AA employer.
E.O. Office: 21 Spruce Hall


From: Peter Monk <>
Date: Tue, 6 Dec 1994 08:59:57 -0500
Subject: Position at University of Delaware

University of Delaware
Department of Mathematical Sciences

The department invites applications for a tenure track assistant
professorship in industrial applied mathematics, to begin September 1,
1995. Candidates should have a Ph.D. and demonstrated research potential
in applied mathematics. Preference will be given to candidates
who have the potential to interact with our applied mathematics faculty
in one of the following areas:
* fluid dynamics (transonic aerodynamics, viscoelasticity);
* inverse problems (tomography and scattering);
* wave propagation (acoustic and electromagnetic);
* scientific computing;
* solid mechanics (elasticity, thermoelasticity).

A commitment to teaching is essential. Preference will be given to
those candidates who evidence experience and/or ability in developing
research links and student internships with industry (preferably in the
Mid-Atlantic region) or national laboratories.

Applicants should send a curriculum vitae, reprints and preprints,
and arrange to have 3 letters of reference sent to Professor Ralph
Kleinman, Search Committee, Department of Mathematical Sciences, University
of Delaware, Newark, DE 19716 by January 15, 1995 for full consideration.

The University of Delaware is an equal opportunity/affirmative action


From: Jack Dongarra <>
Date: Sat, 10 Dec 1994 16:55:20 -0500
Subject: Position at University of Tennessee

Position available at the University of Tennessee
C++ Library for Linear Algebra

A research position is available in parallel scientific software
at the University of Tennessee. Researchers at the University of
Tennessee, the University of California-Berkeley, UCLA, Rice University,
Oak Ridge National Laboratory, and the University of Illinois are
engaged in a cooperative research and development project to extend
the linear algebra library LAPACK for high-performance computers.
The goals of the project, called ScaLAPACK, are producing a core set of
routines based on LAPACK for distributed-memory computers, developing
Fortran 90 and C++ language versions of some of the most important
subroutines, writing versions of several subroutines to exploit special
properties of IEEE arithmetic, and extending the capabilities of the
existing LAPACK package in areas such as the solution of Sylvester
equations and the generalized singular value decomposition.

The principal investigators are Jack Dongarra at the University of
Tennessee and Oak Ridge National Laboratory, Jim Demmel at Berkeley,
Tony Chan at UCLA, Danny Sorensen at Rice, Mike Heath at the University
of Illinois, and David Walker at Oak Ridge National Laboratory.

The position involves numerical analysis and scientific programming.
Familiarity with C++, parallel architectures and algorithms is also desired.
Additional benefits of the position include a competitive salary,
travel opportunities, access to state-of-the-art computational facilities
(including both parallel architectures and high-performance workstations),
and collaborative research opportunities in a very active research
program in advanced scientific computing.

Inquiries should be directed to:

Jack Dongarra
Computer Science Department
University of Tennessee
Knoxville, TN 37996-1301
Phone: 615-974-8295
Fax: 615-974-8296


End of NA Digest