-------------------------------------------------------
From: Gene Golub <golub@sccm.Stanford.EDU>
Date: Thu, 24 Nov 94 11:44:09 PST
Subject: Flaw in Pentium Chip
In NY Times for Nov. 24, there is an article by John Markoff describing
an error in division operation of the Pentium chip made by INTEL. (The
article is on the business pages which seems to be where most computer
announcements are made!) There are quotes by Velvel Kahan and Cleve
Moler (there is also a photo of Cleve). I think it is good to call
such problems to the attention of our colleagues and students.
It would be good if we could help the manufacturers in debugging
their chips before they are released. Thank goodness we have
the efforts of Kahan but we need a more concerted effort.
Gene
------------------------------
From: Cleve Moler <moler@mathworks.com>
Date: Mon Nov 28 22:13:20 EST 1994
Subject: The Pentium Division Bug
Hi, all --
I've been unusually busy the last week. I would like to write
something specially for the NA Digest that explains why, but
I'm afraid I don't have enough time tonight. Maybe I can do
something by next week. In the meantime, you might go browsing
through the following.
-- Cleve
Pentium Papers Repository
The MathWorks is making a collection of "primary source" material on
the Pentium division bug available. If you're wired to the Web, try
www.mathworks.com -- "What's New" button
or, with anonymous FTP, try
ftp.mathworks.com -- directory /pub/tech-support/moler/Pentium
The documents available as of today, 11/28/94, are listed below.
This archive is intended as a reasonably complete historical record of
the events associated with the Pentium floating point division bug.
All of these documents are reproduced as they originally appeared on the
Net or elsewhere with full credit given to the authors and institutions
involved. Some material may be copyrighted and should be treated as such.
Nicely_original_post.txt
October 30. Memo from Prof. Thomas Nicely, Lynchburg College.
Calculations involving prime numbers lead to the first
description of the bug. Example is 1/824633702441.
Mathisen_first_post.txt
October 30. A series of Internet postings by Terje Mathisen,
Norsk Hydro, Norway, confirming the bug and lead to a test
program, p87test.zip.
EE_Times.txt
November 7. Article by Alex Wolfe in the EE Times, a weekly
trade publication with the headline,
INTEL FIXES A PENTIUM FPU GLITCH
Copyright (c) 1994 by the EE Times
Coe.txt
November 15. Internet posting by Tim Coe, Vitesse
Semiconductor, with a model of the chip's behavior and
the example 4195835/3145727.
Moler_first_post.txt
November 15. Internet posting by Cleve Moler, the MathWorks,
summarizing results to date. Examples include Nicely's prime
reciprocal and Coe's ratio.
Cable_News_Network.txt
November 22. Report by Steve Young on CNN's Moneyline includes
interviews with Intel's Stephen Smith and Moler.
MathWorks_press_release.txt
November 23. MathWorks issues a press release with the title
THE MATHWORKS DEVELOPS FIX FOR THE INTEL PENTIUM(tm) FLOATING
POINT ERROR
New_York_Times.txt
November 24. New York Times article by John Markoff with headline
CIRCUIT FLAW CAUSES PENTIUM CHIP TO MISCALCULATE, INTEL ADMITS
Copyright (c) 1994 by the New York Times
Associated_Press.txt
November 24. News story circulated by the Associated Press.
Copyright (c) 1994 by the Associated Press
Moler_second_post.txt
November 24. Internet posting by Moler describing a software/
hardware workaround for the FDIV bug.
Moler_third_post.txt
November 24. Internet posting by Moler announcing a Pentium-Aware
Release of MATLAB.
Intel_support.txt
November 24. America OnLine and Internet posting by
Ken Hendren, Intel Applications Support Manager.
Intel_FAX.txt
Intel FAXBACK Document #7999
Obtained from FAXBACK system at 800 628-2283
Nicely_second_post.txt
November 25. Memo from Prof. Nicely entitled "Pentium Bug
and the Intel NDA".
Andy_Grove.txt
November 27. Internet posting by Intel CEO Andy Grove entitled
"My Perspective on Pentium".
------------------------------
From: Ulrich Ruede <ruede@informatik.tu-muenchen.de>
Date: Mon, 21 Nov 1994 19:30:11 +0100
Subject: German Scientific Computing Home Page
German Scientific Computing Home Page
We have recently started to provide a collection of WWW
pages accessible via URL
http://www5.informatik.tu-muenchen.de/sci-comp/home.html
These documents collect information about Scientific Computing in Germany.
We invite the active participation of the Scientifc Computing Community
both within Germany and internationally. All feedback to
scicomp@informatik.tu-muenchen.de
is welcome.
Please help to make this service useful by sending us the information
you have!
Uli Ruede
Ulrich Ruede
Institut fuer Informatik, Technische Universitaet,
D-80290 Muenchen, Germany, e-mail: ruede@informatik.tu-muenchen.de
Tel: +49 89 21058238, Fax: +49 89 21052022
URL: http://www5.informatik.tu-muenchen.de/persons/ruede.html
------------------------------
From: bpohl@sam.math.ethz.ch
Date: Tue, 22 Nov 94 18:51:47 +0100
Subject: FTP Reports from SAM at ETH Zuerich
The Seminar fuer Angewandte Mathematik (SAM)
at
ETH Zuerich
now has an anonymous ftp-site from which you can ftp the
research reports, published at SAM.
To get there type
ftp ftp.sam.math.ethz.ch
Then login as anonymous, give your e-mail address as a password, then
cd pub/sam-reports
You can get the file README
and follow the instructions given in that file.
If you have difficulties, questions or suggestions please contact
Nicholas D. Ironmonger
SAM
ETH Zuerich
CH-8092 Zuerich
Tel: ++41 - 1 632 23 57
FAX: ++41 - 1 632 10 85
e-mail: ndi@sam.math.ethz.ch
------------------------------
From: Plamen Yalamov <bterer%BGCICT.BITNET@utkvm1.utk.edu>
Date: Thu, 24 Nov 1994 12:53:09 +0200
Subject: MATLAB Code for Integer Programming
Dear NA-NETers,
Is anyone aware of a MATLAB code for INTEGER PROGRAMMING ?
I have the Optimization Toolbox but there is nothing in
this toolbox. Could anyone send such a piece to me if it is free?
Plamen Yalamov
------------------------------
From: Walter Lioen <Walter.Lioen@cwi.nl>
Date: Mon, 28 Nov 1994 15:59:01 GMT
Subject: Call for IVP Test Set Problems
We, the Initial Value Problem group of Peter van der Houwen of the
numerical mathematics department of CWI, Amsterdam are working on
parallel ODE/DAE solvers in a project called `Parallel Codes for
Circuit Analysis and Control Engineering'.
At present we have parallel codes for ODEs and we are at the point of
adding the DAE part. However, for both categories of problems we have
a lack of good (i.e., large and difficult) test problems.
Presently Alfredo Bellen at Triest is composing a test set. This set
will be our point of departure, but we want to extend this test set.
If we succeed in this effort, both a descriptive report, and problem
sources, will be made available by anonymous ftp.
We are interested in:
- real life problems, for example but not limited to
electrical circuits, chemical reactions, control engineering;
- preferably published in the open literature;
- stiff (at least, on parts of the integration interval);
- high dimension (100-1000 or even larger);
- for the DAEs, the index should be restricted to 2;
- because of the desired dimension some machine readable format
preferably Fortran source but C, Pascal and Maple are also
welcome;
- all you can tell us about the solution;
- permission to make it publically available
(of course with the proper acknowledgements).
If you can not fulfil all of our wishes, but got the point, please
do not hesitate to react.
The project's group members are:
Peter J. van der Houwen <senna@cwi.nl> project leader,
Walter Hoffmann <walter@fwi.uva.nl> second project leader,
Ben P. Sommeijer <bsom@cwi.nl> senior researcher,
Jacques J.B. de Swart <jacques@cwi.nl> PhD. student,
Wolter van der Veen <jacques@cwi.nl> PhD. student,
Walter M. Lioen <walter@cwi.nl> scientific programmer.
Walter Hoffmann is of the University of Amsterdam.
All other members are working at CWI.
Please send a small description of what you could offer
(and how you score on our overcharged wish list)
to one of: bsom@cwi.nl, jacques@cwi.nl, wolter@cwi.nl.
Thanks in advance,
Walter M. Lioen
CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands.
e-mail: walter@cwi.nl phone: +31 20 5924101
fax: +31 20 5924199 telex: 12571 mactr nl
------------------------------
From: Lieven Vandenberghe <Lieven.Vandenberghe@esat.kuleuven.ac.be>
Date: Fri, 25 Nov 1994 09:26:15 +0100
Subject: Software for Semidefinite Programming
Semidefinite Programming
Software and Survey Paper available
In semidefinite programming we minimize a linear function subject
to the constraint that an affine combination of symmetric matrices
is positive semidefinite. Semidefinite programming unifies several
standard problems (e.g., linear and quadratic programming) and
finds many applications in control, structural optimization,
combinatorial optimization, and other fields. Although semidefinite
programs are much more general than linear programs, they can be
solved as efficiently. Most interior-point methods for linear
programming have been generalized to semidefinite programs.
As in linear programming, these methods have polynomial worst-case
complexity, and perform very well in practice.
A software package and a survey paper are now available via
anonymous ftp. The software consists of C-source that calls
LAPACK and also some matlab routines that work with a mex-file
interface.
To get the software, ftp as anonymous to isl.stanford.edu, and
cd to pub/boyd/semidef_prog. Set binary mode and get the file
semidef_prog.tar.Z (which includes semidef_prog.ps.Z, the
corresponding survey paper), and the appropriate mex-file. Quit ftp.
Uncompress and untar semidef_prog.tar.Z:
your-machine> zcat semidef.tar.Z | tar xvf -
You will then have a directory semidef which contains source code,
postscript documentation, source for matlab mex interfaces,
and example matlab files.
You can get the survey paper alone in pub/boyd/reports, in the
file semidef_prog.ps.Z. You may also be interested in several
related papers available via anonymous ftp in pub/boyd/reports,
e.g., pri_dual.ps.Z, mit-talk.ps.Z, ifac_eng_des.ps.Z.
Lieven Vandenberghe (K.U. Leuven)
Stephen Boyd (Stanford University)
------------------------------
From: M. Abouziarov <ABOUZIAROV@IIEVMS1.IIECUER.UNAM.MX>
Date: Fri, 25 Nov 1994 14:08 -0600
Subject: Modified Godunov Methods
Dear frends.
I have read your e-mail address in internet system and decided
to write you such letter:
I am mathematician from Russia, my name is Moustafa Abouziarov.
I have graduated from Moscow Physical-Technical Institute in 1981,
received doctor's degree in 1990, now I work in Mexico.
I am a specialist in numerical methods of continuum mechanics,
especially in Godunov's method , and the major result of my
scientific work is the modification of this well-known difference
The advantages of my modification of Godunov's
method are:
1. the second order accuracy in space and time is achieved
for the case of two and three 3-D variables, one must
account also for the variations due to the transversal
gradients;
2. no increase of the adjacent cell number is required for
analyzing the cell;
3. there is no difference between Euler case and Lagrang one.
4. the second order is achieved on the irregular and
moving meshes,where Godunov's method does not provide
even the first-order accuracy;
5. introduction of the first-order scheme predictor step
after the analysis of the spline for pressure makes it
possible to avoid non-physical oscillations;
6. the second-order approximation on the "rigid wall"- type
boundary is achieved;
7. no substantional modifications of the present software
systems ,based on Godunov's method, are required;
8. the controlled viscosity makes it possible to handle the
Navier-Stokes equations,using the scheme for the Euler
equations;
9. the approach is easily extended to the versions of Godu-
nov's method for simulating the elastic-plastic flows and
handling the Timoshenko-type shell equations.
10. the present modifications is essentially effective to analyze
3-D problems of high-energy shocks in fluids and gases and
the hypersonic flows.
I used this modification of Godunov's method to analyze 2-D
problems of high-energy shocks,generated by detonation of solid
explosive, in fluids and gases in elastic-plastic tanks. I
received reliable results.
Then I have extended my modification for nonlinear case. In
this case it is necessary to take into account some nonlinear
properties of Riemann's problem solution and the quadratic
spline for density.
My results are similar or better than [1].
But I have some problem, I think you know it.
If I solve the test from [1] about interaction of two blast wave as
a two-dimensional problem ( X is direction of propagation of waves)
with the rigged walls on Y=Y0 and on Y=Y1 (conservative boundary
conditions on Y direction) on Y direction I receive some
oscillations of pressure and density and I receive Y direction
velocity. The altitude of this oscillations may be about 10%
or more for pressure. Somebody calls it as nonlinear nonstability.
I do not know how to avoid this nonphysical oscillations. They are
generated by rigged body boundary conditions.
So I would like to have contact with specialists in this area
to solve this and some other problems, conserning modifications of
Godunov's method for some other kinds of equations, lenearized
Navier-Stokes equations for example, different state equations
and etc. If you know e-mails addresses of such specialists
( [1] and etc.) in USA and etc., please, send me them.
[1] Colella P. and Woodword P. The Piecewise Parabolic method
for Gas-Dynamical Simulations. // J. Comp. Phys. 1984.
V. 54. P. 174 - 202.
My e-mail address: < abouziarov@iievms1.iiecuer.unam.mx >
Best regards
M.Abouziarov.
------------------------------
From: Gene Golub <golub@sccm.Stanford.EDU>
Date: Sun, 20 Nov 94 17:49:07 PST
Subject: NA Summer School -- 1995: 2nd Announcement
AMS-SIAM Summer Seminar in Applied Mathematics
"Mathematics of Numerical Analysis: Real Number Algorithms"
Park City, Utah, July 17--August 11, 1995
The twenty-fifth AMS--SIAM Summer Seminar in Applied Mathematics will
be held July 17--August 11, 1995 at the Prospector Square Inn and
Conference Center, Park City, Utah. The seminar will be sponsored by
the American Mathematical Society, the Society for Industrial and
Applied Mathematics, and the International Mathematical Union. It is
anticipated that the seminar will be partially supported by grants
from federal agencies. The proceedings will be published by the AMS
in the "Lectures in Applied Mathematics" series.
The mathematical theory of real number algorithms is to be the subject
of this proposed conference. Thus numerical analysis will be central
with emphasis on geometrical, algebraic, analytic, and foundational
perspectives. Investigations of efficiency will play a special role.
Practical algorithms will be the subject of theoretical analysis, but
immediate useful results will not be demanded.
It is hoped that the conference will give the subject of numerical
analysis a greater coherence through a focus on the mathematical side.
In particular, to aim to strengthen the unity of mathematics and
numerical analysis, and to narrow the gap between pure and applied
mathematics. That goal is appropriate since many of the heroes of
pure and applied mathematics, Newton, Euler, Lagrange, and Gauss among
them, established the basic real number algorithms. With the
revolution of the computer and the great achievements of scientific
computation, it does service to both the pure and applied communities
to support the mathematical development of numerical analysis.
This is an appropriate time to schedule such a meeting in view of the
rapid development of heuristic work, a good base of theoretical work,
and a widespread desire for mathematical deepening of the subject.
The conference will be international in character with strong
representation from the most mathematically developed parts of
numerical analysis. Besides tutorials and short courses, seminars in
the following areas are contemplated: linear algebra, nonlinear
systems-path following, differential equations, linear programming
problems, algebraic questions, foundations, information based
complexity, lower bounds, and approximation theory.
The organizing committee includes
Eugene L. Allgower, Colorado State University;
Lenore Blum, MSRI;
Alexandre J. Chorin, University of California, Berkeley;
Philippe G. Ciarlet, Universit\'e Pierre et Marie Curie, Paris;
Felipe Cucker, Universitat Pampeu Fabra, Spain;
James W. Demmel, University of California, Berkeley;
Ronald A. DeVore, University of South Carolina, Columbia;
Gene H. Golub, Stanford University;
Arieh Iserles, University of Cambridge, UK;
Hubertus Th. Jongen, Reinisch-Westf Tech Hochschule, Aachen,
Germany;
Herb Keller, California Institute of Technology;
Jacques Louis Lions, College de France;
James M. Renegar, Cornell University;
Steve Smale (Chair), University of California, Berkeley;
Michael Shub, IBM;
Gilbert Strang, MIT;
Shmuel Winograd, IBM; and
Henryk Wozniakowski, University of Warsaw and Columbia
University.
To date the following have accepted invitations to speak:
All members of the organizing committee;
Roger Brockett, Harvard University;
John Canny, University of California, Berkeley;
W. Dahmen, Reinisch-Westf Tech Hochschule, Aachen, Germany;
David Donoho, University of California, Berkeley;
James G. Glimm, SUNY at Stony Brook;
N. Karmarker, A T & T Bell Laboratories;
T. Y. Li, Michigan State University;
Arkadi Nemirovski, Israel Institute of Technology;
Victor Pan, Herbert H. Lehman College, CUNY;
Vladimir Rokhlin, Yale University;
Marie-Francoise Roy, Universit\'e de Rennes;
Roger Temam, Indiana University;
Richard S. Varga, Kent State University;
Victor A. V. Vassiliev, Institute for System Studies, Moscow;
Margaret H. Wright, A T & T Bell Laboratories;
Yosef Yomdin, Weizmann Institute of Science, Israel;
Mike Powell, Cambridge; and
D. Grigoriev, Penn State (Tentative).
Park City is a popular summer vacation destination with a comfortable,
temperate climate in the mountains of Utah. Housing for participants
has been arranged at the Prospector Square Inn and Conference Center.
Inexpensive restaurants, food shops, and other attractions are within
walking distance of the Inn. The Prospector Square Inn includes eight
buildings with rustic ski lodge style accommodations, in addition to a
large lecture hall and meeting rooms. A sports center including pool,
exercise machines, racquetball courts, etc. (all available for an
extra charge) is located on the property. All rooms being held for
participants contain two double- or queen-sized beds, television,
telephone, microwave oven, and refrigerator. Some units have full
kitchens. The daily cost is $45 single or double occupancy ($50
triple and $55 quad) plus 10.25% lodging tax. Note that these prices
are per room, not per person. For those attending the full four weeks
of the seminar, a very limited number of one-, two-, and three-bedroom
condominium units is available on a monthly basis. Those interested
should contact the conference coordinator. More detailed information,
including how to make reservations, will be included with the official
invitation to the seminar.
There is a registration fee of $40. Everyone interested receiving an
invitation to attend should send the following information before
February 15, 1995, to AMS--Summer Seminar Conference Coordinator, AMS
Meetings and Conferences Department, P.O. Box 6887, Providence,
RI 02940; e-mail dls@math.ams.org. Please type or print the following:
1. Full name and mailing address;
2. Telephone number and area code for office and home;
3. E-mail address if available;
4. Anticipated arrival and departure dates;
5. Your scientific background relevant to the topic of the seminar;
please indicate if you are a student or if you received your Ph.D. on or
after 7/1/89;
6. Financial assistance requested (please estimate cost of travel);
indicate if support is not required and if interested in attending
even if support is not offered.
7. Indicate if you would like to be included on a list of those
desiring a roommate for the seminar. If yes, please indicate if you
are male or female, and list any other pertinent information (i.e.,
smoking/nonsmoking).
Special encouragement is extended to junior scientists to apply. A
special pool of funds expected from federal agencies has been
earmarked for this group. Other participants who wish to apply
for a grant-in-aid should so indicate; however, funds available for
the seminar are very limited, and individuals who can obtain support from
other sources should do so. Advanced graduate students
are encouraged to participate.
------------------------------
From: Claudio Canuto <CCANUTO@polito.it>
Date: Mon, 21 Nov 1994 15:20:42 GMT+1
Subject: Seminar on Numerical Methods for PDE in Italy
POLITECNICO DI TORINO ISTITUTO DI ANALISI NUMERICA DEL C.N.R.
Dipartimento di Matematica Pavia
Seminar on
RECENT ADVANCES IN NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
Politecnico di Torino - February 14-16, 1995
TOPICS: adaptivity and a-posteriori error estimates, multi-level techniques
(hierarchical bases, wavelets, non-linear Galerkin methods), discretization
methods for multi-scale phenomena.
INVITED LECTURERS:
R.E.BANK (San Diego) W.DAHMEN (Aachen)
S.JAFFARD (E.N.P.C.) C.JOHNSON (Goteborg)
Y.MADAY (Paris VI) A.T.PATERA (M.I.T.)
R.TEMAM (Orsay) R.VERFUERTH (Bochum)
J.XU (PennState) H.YSERENTANT (Tubingen)
CALL FOR CONTRIBUTIONS: in addition to the invited seminars, a limited
number of short contributions on the themes of the Seminar will be presented.
People interested should submit a title and a one-page abstract to one of
the Organizers BEFORE JANUARY 15, 1995 at the addresses below.
REGISTRATION FEE: a registration fee of 180,000 Italian Lire (reduced to
150,000 It.Lire for members of SIMAI or affiliated organizations, and
to 100,000 It.Lire for students) will be required to cover lunches,
coffee-breaks and social activities.
ACCOMMODATION: Hotel accommodation in Torino will be available at special
discount rates (from 80,000 It.Lire in a **-hotel to 150,000 It.Lire in
a ****-hotel, per single room per day, continental breakfast included).
INFORMATION AND REGISTRATION: People interested in the Seminar should contact
one of the Organizers at the addresses below BEFORE JANUARY 15, 1995,
preferably using fax or e-mail.
ORGANIZATION: The Seminar is organized with the collaboration of SIMAI, ASI,
Cassa di Risparmio di Torino, and other funding institutions.
CLAUDIO CANUTO ALESSANDRO RUSSO
Dipartimento di Matematica Istituto di Analisi Numerica
Politecnico di Torino Consiglio Nazionale delle Ricerche
corso Duca degli Abruzzi, 24 via Abbiategrasso, 209
I-10129 Torino ITALY I-27100 Pavia ITALY
tel. +39 11 564 7543 tel. +39 382 529 600
fax +39 11 564 7599 fax +39 382 529 566
e-mail: ccanuto@polito.it e-mail: russo@dragon.ian.pv.cnr.it
------------------------------
From: Arieh Iserles <A.Iserles@amtp.cam.ac.uk>
Date: Mon, 21 Nov 94 22:05:42 GMT
Subject: Conference on Numerical Mathematics Honoring Mike Powell
Conference on Numerical Mathematics
Celebrating the 60th Birthday of M.J.D. Powell
University of Cambridge, England
27--30 July 1996
The opportunity for this conference is provided by the sixtieth
birthday of one of the world's leading numerical mathematicians, whose
contributions to optimization and approximation have been decisive. The real
purpose, however, is to celebrate numerical mathematics and scientific
computing.
The University of Cambridge, where Mike Powell has been for the last
eighteen years the John Humphrey Plummer Professor of Applied Numerical
Analysis, is a suitable setting for this event. The participants will
be accommodated at historic Magdalene College, in the city centre
of Cambridge.
There will be ten invited, longer lectures that focus on optimization
and approximation theory, but submitted papers, addressing themselves
to original and timely research, are welcome in all fields of
numerical mathematics. We would now like to call for papers to be
presented at this conference. All such papers will be considered for
inclusion into a proceedings. They can be submitted to
either Martin Buhmann or Arieh Iserles, by e-mail or otherwise. Every
submission should contain the title of the talk and an abstract. The
duration of submitted talks will be 25 minutes.
The invited speakers are
Ian Barrodale (Victoria, B.C.)
Carl de Boor (University of Wisconsin at Madison)
Roger Fletcher (University of Dundee)
Gene Golub (Stanford University)
Charles Micchelli (IBM Yorktown Heights)
Jorge More (Argonne National Laboratory)
Beresford Parlett (University of California at Berkeley)
Mike Powell (University of Cambridge)
Mike Todd (Cornell University)
Philippe Toint (University of Namur)
The organizing committee consists of Ian Barrodale (Victoria, B.C.),
Martin Buhmann (ETH Zurich), Wolfgang Dahmen (RWTH Aachen),
Roger Fletcher (University of Dundee), Arieh Iserles (University
of Cambridge), Will Light (University of Leicester), Bill Morton
(University of Oxford), Mike Todd (Cornell University) and Philippe
Toint (University of Namur).
Support for the conference is provided by the London Mathematical Society.
For more information contact:
* M.D. Buhmann
Mathematik Departement
ETH Zentrum
8092 Zurich
Switzerland
E-Mail: mdb@math.ethz.ch
or
* A. Iserles
Department of Applied Mathematics and Theoretical Physics
Silver Street
Cambridge CB3 9EW
England
E-Mail: ai@amtp.cam.ac.uk
------------------------------
From: Robert Gulliver <gulliver@s2.ima.umn.edu>
Date: Wed, 23 Nov 94 12:50:40 CST
Received: by s2.ima.umn.edu; Wed, 23 Nov 94 12:50:40 CST
Subject: Institue for Mathematics and its Applications Winter Tutorials
During Winter, 1995 the Institute for Mathematics and its Applications in
Minneapolis will hold two tutorials on Inverse Problems in Wave Propagation.
The January 17-20 tutorial will emphasise electromagnetic waves, with
applications to tomography and random media; survey talks by David Colton,
Adel Faridani, and George Papanicolaou are planned. The January 30-February 3
tutorial will be more closely relevant to acoustic waves, e.g. as applied in
acoustic microscopy (geophysics) and seismology; the IMA expects to hear
talks from Jan Achenbach, Christof Stork, William Symes and Gunther Uhlmann.
For more information contact ima-staff@ima.umn.edu.
------------------------------
From: J. C. Mason <SCOMJCM@pegasus.hud.ac.uk>
Organization: The University of Huddersfield HEC
Subject: Mathematics of Neural Networks
CALL FOR PAPERS -
MATHEMATICS of NEURAL NETWORKS and APPLICATIONS (MANNA 1995)
International Conference at Lady Margaret Hall, Oxford,
July 3-7, 1995
- run by the Universities of Huddersfield and Brighton
- with support from the London Mathematical Society
We are delighted to announce the first conference on the Mathematics
of Neural Networks and Applications (MANNA), in which we aim to
provide both top class research and a friendly motivating atmosphere.
Applications of neural networks (NNs) have often been carried out with
a limited understanding of the underlying mathematics but it is now
essential that fuller account should be taken of the many topics that
contribute to NNs: approximation theory, control theory, genetic
algorithms, dynamical systems, numerical analysis, optimisation,
statistical decision theory, statistical mechanics, computability and
information theory, etc. .
We aim to consider the links between these topics and the insights
they offer, and identify mathematical tools and techniques for
analysing and developing NN theories, algorithms and applications.
Working sessions and panel discussions are planned.
Keynote speakers who have provisionally accepted invitations include:
N M Allinson (York University, UK) S Grossberg (Boston, USA)
S-i Amari (Tokyo) M Hirsch (Berkeley, USA)
N Biggs (LSE, London) T Poggio (MIT, USA)
G Cybenko (Dartmouth USA) H Ritter (Bielefeld,Germany)
J G Taylor (King's College, London) P C Parks (Oxford)
It is anticipated that up to 40 contributed papers will be presented.
The proceedings will be published, probably as a volume of an
international journal, and contributed papers will be considered for
inclusion. The deadline for submission of abstracts is 17 February
1995.
Accommodation will be available at Lady Margaret Hall (LMH) where many
rooms have en-suite facilities. The conference will start with
Monday lunch and end with Friday lunch, and there will be a full-board
charge (including conference dinner) of about 235 pounds for this
period as well as a conference fee of 195 pounds. We expect to be
able to offer a reduction in fee to those who give submitted papers,
and a very low fee to a number of recommended bona-fide students who
book early.
There will be a supporting social programme, including reception,
outing(s) and conference dinner, and family accommodation may be
arranged in local guest houses.
Committee:
S W Ellacott (Brighton) and J C Mason (Huddersfield) (Organisers) ;
I Aleksander, N M Allinson, N Biggs, C M Bishop, D Lowe, P C Parks,
J G Taylor, K Warwick
For information, contact:
Mrs R.Hawkins, School of Computing and Mathematics,
University of Huddersfield, Queensgate , Huddersfield HD1 3DH
Email: R.Hawkins@hud.ac.uk Phone: 44+(0)484 472150
------------------------------
From: Chris Johnson <crj@sci2.cs.utah.edu>
Date: Thu, 24 Nov 1994 14:06:15 -0700
Subject: SPIE Ill-posed Inverse Problems Symposium
Call for Papers
Experimental and Numerical Methods for Solving Ill-Posed Inverse
Problems: Medical and Nonmedical Applications
Conference Chairs: Randall L. Barbour, SUNY/Brooklyn; Mark J.
Carvlin, Bristol-Myers Squibb Co.; Michael A. Fiddy, Univ. of
Massachusetts/Lowell
Program Committee: David Isaacson, Rensselaer Polytechnic
Institute; Norman J. McCormick, Univ. of Washington; Michael V.
Klibanov, Univ. of North Carolina/Charlotte; Christopher R.
Johnson, Univ. of Utah; Robert V. McGahan, Rome Lab.
Part of SPIE's 1995 International Symposium
July 9-14, 1995
San Diego Convention Center
San Diego, CA
Imaging methods are increasingly being applied to a wide range of
applications that include clinical medicine, geophysics, remote sensing,
and materials testing. Sources can be magnetic, acoustic, electrical, or
electromagnetic in origin. These may be located external to the medium or
inside. Detection modes may or may not be time dependent and can range from
backscatter only to full tomographic measurement schemes. A common feature
complicating many of these methods is the uncertainty regarding the volume
of medium probed by the penetrating or emitted energy. Frequently, this
uncertainty is due to the effects of scattering. Accurate knowledge of the
energy distribution requires information about the medium, which is the
unknown being examined. As a result, useful methods frequently must
consider approximate solutions that represent compromises between
computational effort, physical accuracy of the modeling scheme, and quality
and type of available data.
Principal topics of interest will fall into three main areas:
(1) mathematical aspects of inverse methods (e.g., dealing
with ill-conditioning, limited noisy data, missing phase
information, superresolution, etc.);
(2) modeling methods for forward and inverse scattering
phenomena (e.g., approximate solutions to integral equations of
scattering, finite difference time domain, and projection
tomographic techniques); and
(3) interdisciplinary applications, including clinical
medicine, optics, astronomy, remote sensing, etc.
This conference will bring together leading experts from
universities, medical centers, government laboratories, and
industry to discuss the latest developments in the diverse and
fast developing field.
Chris Johnson, Ph.D.
Department of Computer Science
University of Utah
Email: crj@cs.utah.edu
WWW: http://www.cs.utah.edu/~crj
------------------------------
From: Claude Carasso <carasso@anumsun1.univ-st-etienne.fr>
Date: Mon, 28 Nov 94 16:07:49 +0100
Subject: Conference on Flow through Porous Media
INTERNATIONAL CONFERENCE ON
MATHEMATICAL MODELLING OF
FLOW THROUGH POROUS MEDIA
MAY 22-26, 1995
SAINT-ETIENNE (FRANCE)
ORGANIZING COMMITTEE
A. BOURGEAT, C. CARASSO (France), R. EWING (USA), S. LUCKHAUS (Allemagne),
A. MIKELIC (France), M. PRIMICERIO (Italie)
FIRST LIST OF PARTICIPANTS
I. AGANOVIC (Croatie), G. ALLAIRE (France), S. ANTONTSEV (Espagne),
M. AVELLANEDA (U.S.A.), C.I. BARENBLATT (Russie), J. BEAR (Israel),
G. CHAVENT (France), J.H. CUSHMAN (U.S.A.), G. DAGAN (Israel),
J. DOUGLAS Jr (U.S.A.), H. ENE (Roumanie), A.FASANO (Italie),
T. GALLOUET (France), I.W. GELHAR (U.S.A.), R. GILBERT (U.S.A.),
J. GLIMM (U.S.A.), R.A. GREENKORN (U.S.A.), A. GUTJAHR (U.S.A.),
U. HORNUNG (Allemagne), S. KOZLOV (France), R. LENORMAND (France)
V.N. MONAKHOV (Russie), G.PANASENKO (France), P.PANFILOV (Russie),
G.PAPANICOLAOU (U.S.A.), M.QUINTARD (France), T.F RUSSEL (U.S.A.),
J.M.THOMAS (France), C.J.VAN DUIJN (Hollande), M.F. WHEELER (U.S.A.),
S.WHITAKER (U.S.A.), Y.C. YORTSOS (U.S.A.), V.ZHIKOV (Russie)
AIM OF THE CONFERENCE
The main goal of this conference is to bring together leading
researchers in the field of modelling flow in porous media and
to provide a forum for discussion on thecurrent state of
modelling.
The conference will address both the pure theoretical question in
modelling and the use of
various models in numerical simulations.
The conference areas of interest focus on :
- Pore scale models, macropores, fractured media, percolation
- Scaling up, averaging, macrodispersion and homogenization
- Filtration of non Newtonian fluids, multiphase flow and contaminant transport
- Free and moving boundary problems
- Geochemical models, reactive porous media
- Numerical simulation of flows and transport phenomena in porous media
SCIENTIFIC PROGRAM AND PUBLICATION
In addition to the invited lectures a number of posters sessions will
take place.
The conference proceedings will be published and will mainly
include the lectures and selected posters. Moreover there will be
a poster session devoted to industrial research activities
REGISTRATIONFEE
Before April 1st / after April 1st
Delegate from a company 2 500 FF 2 900 FF
University Members 1 200 FF 1 500 FF
INFORMATIONS
Congres Milieux Poreux, Analyse Numerique,
23 rue du Dr Paul Michelon
42023 Saint Etienne cedex 2. FRANCE
Tel. : (33) 77.42.15.35-Fax. : (33) 77.25.60.71
e-mail : cmp@anumsun1.univ-st-etienne.fr
For more details please connect by e-mail to :
cmpinfo@anumsun1.univ-st-etienne.fr
or with mosaic, gopher or xgopher at :
gopher://gopher.univ-st-etienne.fr.
------------------------------
From: Daniel Ho <MADANIEL@cphkvx.cphk.hk>
Date: Mon, 21 Nov 1994 10:56:10 +0800
Subject: Positions at City Polytechnic of Hong Kong
City Polytechnic of Hong Kong
(City University of Hong Kong - designate)
The City Polytechnic of Hong Kong is a well established degree-
granting institution in Hong Kong funded by the government
through the University and Polytechnic Grants Committee. Its
current student population is 15,158 and the number is expected
to grow to 16,000 by the mid-1990's. The Polytechnic is
committed to excellence in teaching and research and to a close
relationship with the community and industry. The medium of
instruction is English. Applications are invited for the
following posts:
University Lectures
Department of Mathematics [Ref.A/164/43]
The Department is seeking applicants for two positions to begin
in September 1995. One position is for a Numerical analyst
specialized in numerical solution of partial differential
equations and the other position can be in any field of Applied
Mathematics. Applicants should have a PhD in Mathematics or a
related discipline with strong research record or excellent
research potential as well as a commitment to teaching
undergraduate and postgraduate students.
Salary: HK$34,415 - $57,490 per month
(Exchange rate: US$1 = HK$7.8 approximately)
Appointment may be on superannuable terms with provision for
retirement benefit or on a fixed term contract with gratuity
payable at 15% of basic salary upon completion of contract.
Generous fringe benefits include medical and dental schemes, long
leave and housing assistance where applicable.
Further information can be obtained from the Personnel Office,
City Polytechnic of Hong Kong, Tat Chee Avenue, Kowloon,
Hong Kong
(Fax: 852-7881154/852-7889334, E-mail: PORECRUT@CITYU.EDU.HK)
or from Professor Roderick S.C. Wong, Head of Department of
Mathematics (E-mail: MAWONG@CITYU.EDU.HK). Please apply with
a curriculum vitae including a list of publications, a statement
describing current and planned research, and the names and
addresses of three academic referees to the Personnel Office by
the end of February 1995.
------------------------------
From: Loki Jorgenson <loki@pecos.cecm.sfu.ca>
Date: Sun, 20 Nov 1994 23:44:52 -0800 (PST)
Subject: Positions at Simon Fraser Centre
SIMON FRASER CENTRE FOR EXPERIMENTAL AND CONSTRUCTIVE MATHEMATICS
(For more information on the Centre's activities, see the CECM prospectus
available through the CECM Information Services at gopher.cecm.sfu.ca
or http://www.cecm.sfu.ca)
The Centre is soliciting applications for one or two POST-DOCTORAL
FELLOWS and/or RESEARCH ASSOCIATES commencing after July 1, 1995, in
any areas compatible with the interests of the centre (specifically
aspects of computationally assisted mathematical analysis, number
theory and discrete mathematics). Applicants with a PhD in Mathematics,
Computer Science or Operations Research will be favoured.
The PDFs are primarily research positions though some teaching may be
involved. Research associates may be involved in significant software
development. Applicants should send a curriculum vitae and arrange for
three letters of reference to be sent to Dr. J.M. Borwein, Director
CECM, Department of Mathematics and Statistics, Simon Fraser
University, Burnaby B.C., V5A 1S6. Applicants should list relevant work
and educational experience; interested candidates should look at the at
the Centre's prospectus for more information (see above).
For RESEARCH ASSOCIATES a strong background in computing is preferred
with a knowledge of FORTRAN, LISP, C or C++ (as well as OOP) considered
an asset although not essential. A familiarity with mathematical
problem-solving platforms (such as MATLAB, Maple, Mathematica, Macsyma,
MuPAD, Pari, etc.), either as a user or as a programmer, is also helpful.
This Centre located in Burnaby, British Columbia (Greater Vancouver) is
dedicated to further research and graduate education in Computation in
the Mathematical Sciences. The Centre provides a sophisticated mix of
computation, experimentation and mathematics. Of interest are questions
on how one uses the computer: To build intuition? To generate
hypotheses? To validate conjectures or prove theorems? To discover
nontrivial examples and counter-examples?
The steering committee consists of J. Borwein (Director), P. Borwein,
L. Goddyn, L. Jorgenson, R. Russell, and M. Trummer. Inquiries may be
directed to J. Borwein at the CECM or via Email to jborwein@cecm.sfu.ca.
------------------------------
From: Markus Hegland <marcus@thrain.anu.edu.au>
Date: Wed, 23 Nov 1994 12:45:03 +1100
Subject: Positions at the Australian National University
THE AUSTRALIAN NATIONAL UNIVERSITY
SCHOOL OF MATHEMATICAL SCIENCES
CENTRE FOR MATHEMATICS AND ITS APPLICATIONS
POSTDOCTORAL FELLOW/RESEARCH FELLOW
( LEVEL A/LEVEL B)
IN ADVANCED COMPUTATION
Applications are invited for appointment to a position at the level of
Postdoctoral Fellow or Research Fellow in the Advanced Computation and
Modelling Program of the Centre for Mathematics & its Applications. The
current research interests of the program includes mathematical software
research and development, numerical methods for partial differential
equations optimization including applications to statistical computing, and
inverse problems.
Appointments will be made for periods of up to three years and may be
extended. The initial level of appointment, depending on the candidate's
experience and qualifications, will lie within the following salary ranges:
Postdoctoral Fellow [Level A] $36,795-$39,495 p.a.
Research Fellow [Level B] $41,574-$49,370 p.a.
Assistance with relocation expenses may also be provided.
Part-time appointment may be available as well as an extended visiting
appointment during a period of leave of absence from a home institution.
Enquires and requests for further information including selection criteria
can be addressed to Professor M R Osborne (email
Mike.Osborne@maths.anu.edu.au Fax 06 2490759). Professor Osborne can be
contacted at Texas A&M University until December 16 1994 (email
mike@cs.tamu.edu).
Closing Date: 23 January 1994 Ref: SMS 15.11.1
Email addresses and/or fax numbers should be provided for referees so that
appointment procedures can be expedited.
APPLICATIONS addressing the selection criteria should be submitted in
duplicate to The Secretary, The Australian National University, Canberra,
ACT 0200 quoting reference number and including curriculum vitae, list of
publications and names and addresses of at least three referees. Further
information is available from either of the contacts listed above. The
University has a "no smoking" policy effective in all University buildings
and vehicles.
------------------------------
From: Gal Berkooz <gal@cam.cornell.edu>
Date: Tue, 22 Nov 1994 22:41:19 -0500
Subject: Position at BEAM in Ithaca, NY
BEAM
Engineering and Applied Research
205 W. Court St.
Ithaca, New York 14850
Employment Opportunity
Research & Development
Scientist / CFD-Flow
Optimization
Status: Full time exempt position. Supervision received: Reports to President/Project Leader.
Supervision exercised: Scientific programmers/None. Date posted: 11/16/1994. Start Date:
2/1/1995 or when qualified applicant is selected. Location: Ithaca, NY.
Job Summary: Develop and modify production CFD codes with turbulence models to perform flow
analysis and flow optimization. Work to integrate CFD-Flow Optimization software into other
software products. Participate in the development of flow analysis and other scientific software.
Participate in solving and analyzing specific configurations related to jet flows and complex
geometry nozzles. Write technical reports and present results to government and industry concerns.
Competency Required: Ability to develop high quality numerical codes. Ability to integrate
developed code with other existing software. Ability to independently initiate and pursue technical
objectives. Excellent communications and team-working skills.
Education/Experience Required: A Ph.D. in fluids mechanics or applied mathematics involving
the development and application of flow optimization codes or equivalent work experience. At least
two years of post-doctoral work or equivalent experience required. Applications from promising
recent graduates will be considered. Experience in industry a plus. Experience with numerical
analysis, and analyzing and choosing algorithms. Some experience with generating geometries for
complex configurations. Experience with development of GUIUs a plus.
Salary and Benefits: Salary of $45,000-$65,000 commensurate with qualifications and experience.
BEAM offers a comprehensive benefits package and stock ownership programs. Ithaca offers a low
cost of living and a high quality of life.
Send resume to:
President
BEAM Engineering and Applied Research
c/o Search 102
205 W. Court St.
Ithaca NY 14850
------------------------------
From: C.B. Vreugdenhil <C.B.Vreugdenhil@fys.ruu.nl>
Date: Wed, 23 Nov 1994 09:51:35 +0100
Subject: New Book on Numerical Methods for Shallow-water Flow
New book.
Numerical methods for shallow-water flow
by C.B. Vreugdenhil
Kluwer Academic Publishers, Dordrecht 1994
ISBN 0-7923-3164-8
261 pages
Price Dfl 185
Shallow-water problems occur in a wide variety, such as atmospheric flows,
tides, storm surges, river and coastal flows, lake flows, tsunamis.
Numerical simulation is an effective tool to solve them and a great
variety of numerical methods are available. The first part of the book
summarizes the basic physics of shallow-water flow needed to use numerical
methods in various conditions. The second part gives an overview of
possible numerical methods, not only with their stability and accuracy
properties but also with an assessment of performance in various
conditions. This enables the reader to make a choice for particular
applications. Correct treatment of boundary conditions (often
neglected) is emphasized. The greater part of the book is about
two-dimensional shallow-water equations but a discussion of the 3-d
form is included. The book is intended for researchers and users
of shallow-water models in oceanographic and meteorological institutes,
hydraulic engineering and consulting. It also provides a major
source of information to applied and numerical mathematicians.
Contents:
1. Shallow-water flows
2. Equations
3. Some properties
4. Behaviour of solutions
5. Boundary conditions
6. Discretization in space
7. Effects of space discretization on wave propagation
8. Time integration methods
9. Effect of time integration on wave propagation
10. Numerical treatment of boundary conditions
11. Three-dimensional shallow-water flow
C.B.Vreugdenhil
Institute for Marine and Atmospheric Research Utrecht (IMAU)
Princetonplein 5
3584 CC Utrecht
The Netherlands
phone +31 30 533167
fax +31 30 543163
email vreugdhl@fys.ruu.nl
------------------------------
From: Ron Boisvert <boisvert@cam.nist.gov>
Date: Mon, 21 Nov 94 17:32:04 EST
Subject: Contents, Transactions on Mathematical Software
(Note : Information on TOMS, including complete searchable Table of
Contents of all volumes and upcoming papers, is available on the
World Wide Web at http://gams.nist.gov/toms/.)
Table of Contents
ACM Transactions on Mathematical Software (TOMS)
Volume 20, Number 3 (September 1994)
Patrick F. Cummins and Geoffrey K. Vallis,
Algorithm 732: Solvers for Self-Adjoint Elliptic Problems in
Irregular Two-Dimensional Domains,
pp. 247-261.
Dieter Kraft,
Algorithm 733: TOMP -- Fortran Modules for Optimal Control
Calculations,
pp. 262-281.
Victoria Z. Averbukh and Samuel Figueroa and Tamar Schlick,
Remark on Algorithm 566,
pp. 282-285.
Jorge More and David J. Thuente,
Line Search Algorithms With Guaranteed Sufficient Decrease,
pp. 286-307.
A. G. Buckley,
Conversion to Fortran 90: A Case Study,
pp. 308-353.
A. G. Buckley,
Algorithm 734: A Fortran 90 Code for Unconstrained Nonlinear
Minimization,
pp. 354-372.
K. Kim and J.L. Nazareth,
A Primal Null-space Affine Scaling Method,
pp. 373-392.
Barry W. Brown and Lawrence Levy,
Certification of Algorithm 708: Significant Digit Computation of the
Incomplete Beta,
pp. 393-397.
Carl Taswell and Kevin C. McGill,
Algorithm 735: Wavelet Transform Algorithms for Finite Duration
Discrete-Time Signals,
pp. 398-412.
------------------------------
From: SVJPS@vax.ntp.springer.de
Date: Tue, 22 Nov 1994 21:26:06 +0000 (N)
Subject: Springer Verlag Journals Preview Service
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CC Numerische Mathematik ISSN 0029-599X
CC Volume 69 Number 1 (1994) code 211 file T4069001.211
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CC R.S. Varga, Kent
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AU Axelsson-O. Chronopoulos-A-T.
TI On nonlinear generalized conjugate gradient methods.
SO Numer.-Math.. 1994 69(1) P 1.
AB 40690001.211
AU Elsner-L. He-C. Mehrmann-V.
TI Minimizing the condition number of a positive definite matrix by
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SO Numer.-Math.. 1994 69(1) P 17.
AB 40690017.211
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TI Using the L--curve for determining optimal regularization
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AB 40690025.211
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TI Paraxial approximation of ultrarelativistic intense beams.
SO Numer.-Math.. 1994 69(1) P 33.
AB 40690033.211
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TI Local convergence of the (exact and inexact) iterative aggregation
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SO Numer.-Math.. 1994 69(1) P 61.
AB 40690061.211
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TI Error estimates for the approximation of semicoercive variational
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SO Numer.-Math.. 1994 69(1) P 103.
AB 40690103.211
AU Zerner-M.
TI An asymptotically optimal finite element scheme for the arch
problem.
SO Numer.-Math.. 1994 69(1) P 117.
AB 40690117.211
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------------------------------
From: Kearfott R. Baker <rbk5287@interval.usl.edu>
Date: Wed, 23 Nov 1994 09:52:04 -0600
Subject: Contents: Interval Computations;
Interval Computations. - 1994. - N 1. - 116 p.
CONTENTS
Mathematical Research
G. Alefeld and G. Mayer
A Computer Aided Existence and Uniqueness Proof
for an Inverse Matrix Eigenvalue Problem 4
W. J. Luther and W. Otten
Verified Inclusion for Eigenvalues of Hill's Equation 28
G. L. Kozina and V. A. Perepelitsa
Interval Spanning Trees Problem:
Solvability and Computational Complexity 42
H. Schwandt
Suboptimal Enclosures for the Interval Buneman Algorithm
for Arbitrary Block Dimension 51
O. B. Ermakov
Solving Systems of Ordinary Differential Equations Using
Adams' Interpolation Method with Guaranteed Accuracy 90
Teaching
G. G. Menshikov
On Different Definitions of Interval Extension:
Problems of Teaching 96
Amendment 99
Bibliography
Bibliography of Soviet Works on Interval Computations.
Part V 100
Requirements for manuscript preparation 110
Requirements for manuscript preparation (in Russian) 111
Addresses of the editorial board members 112
Contents 114
OTHER NEWS:
An updated preliminary program, as well as registration and hotel reservation
forms for the
International Workshop on Applications of Interval Computations
have been placed in the anonymous ftp area of
interval.usl.edu
------------------------------
From: Ake Bjorck <akbjo@math.liu.se>
Date: Wed, 23 Nov 94 17:24:22 +0100
Subject: Contents, BIT
CONTENTS
BIT Volume 34, No. 4 (1994)
ISSN 0006-3835
Modeling and velocity stabilization of constrained mechanical systems
Taifun Alishenas and \"Orn {\'O}lafsson, pp. 455--483
Finding minimum height elimination trees for interval graphs in
polynomial time
Bengt Aspvall and Pinar Heggernes, pp. 484--509
An implicit shift bidiagonalization algorithm for ill-posed problems
{\AA}ke Bj\"orck, Eric Grimme, and Paul Van Dooren, pp. 510--534
On the convergence of the multivariate ''homogeneous'' QD-algorithm
Annie Cuyt, pp. 535--545
Theoretical and practical efficiency measures for symmetric interpolatory
quadrature formulas
Paola Favati, Grazia Lotti, and Francesco Romani, pp. 546--557
Least squares fitting of circles and ellipses
Walter Gander, Gene H. Golub, and Rolf Strebel, pp. 558--578
Preconditioning strategies for asymptotically ill-conditioned block Toeplitz
systems
Stefano Serra, pp. 579--594
Acknowledgements of referees p. 595
Index Volume 34 pp.596--598
BIT now accepts papers in LaTeX. For information send email to
the Editor:
{\AA}ke Bj\"orck
Department of Mathematics
Link\"oping University
S-581 83 Link\"oping, Sweden
E-mail: akbjo@math.liu.se
FAX: +46-13 100 746
------------------------------
End of NA Digest
**************************
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