NA Digest Sunday, April 22, 1990 Volume 90 : Issue 16
Today's Editor: Cleve Moler
Today's Topics:
-------------------------------------------------------
From: Gene H. Golub <golub@na-net.stanford.edu>
Date: Sat, 21 Apr 1990 15:35:12 PDT
Subject: David Young's Recovery
I spoke to David Young at his home on Friday. David recently had a
serious operation. His voice was very strong and he seemed very
cheerful and optimistic.
I'm sure he would be pleased to hear from you.
Here is his address and phone numbers.
Prof. David M. Young, Jr.
Ashbel Smith Professor, Math & Comp Cntr
young@cs.utexas.edu
Center for Numerical Analysis
RLM 13.150
The University of Texas at Austin
Austin, Texas 78712
Office Phone: (512) 471-1242
Home Phone: (512) 452-2966
Gene
------------------------------
From: Gene H. Golub <golub@na-net.stanford.edu>
Date: Sat, 21 Apr 1990 17:09:25 PDT
Subject: E-Letter on Systems, Control, and Signal Processing.
For those of you interested in System Science, there is a very nice
newsletter sent on a regular basis. It is known as
E-LETTER on Systems, Control, and Signal Processing.
The editors are
Bradley W. Dickinson
bradley@princeton.edu or bradley@pucc.bitnet
Eduardo D. Sontag
sontag@hilbert.rutgers.edu or sontag@pisces.bitnet.
A msg to one of the editors will get you on the distribution list.
Gene Golub
------------------------------
From: Steven Kratzer <kratzer@super.org>
Date: Wed, 18 Apr 90 10:10:21 EDT
Subject: Review of the Seventh Parallel Circus
Review of the Seventh Parallel Circus
by Steven Kratzer
Supercomputing Research Center, Bowie, MD
The Seventh Parallel Circus was held on Friday and Saturday, March 30
and 31, at Stanford University. The Parallel Circus is an informal
gathering of researchers interested in parallel processing for
numerical computing. This event is held twice a year; past Circuses
were held at various locations in the Eastern US, but this time the
beautiful (and relatively warm) Stanford campus was chosen. The participants
represented a variety of campuses, companies and organizations from
throughout North America and Scandinavia.
The meeting was organized by Gene Golub of Stanford, and Steve
Hammond and Rob Schreiber of RIACS. About sixty people attended,
and there were around 20 talks (nominally 20 minutes each, with
plenty of time for discussions). The talks covered a wide spectrum,
from mathematics and graph theory to chip design,
and many of them contained brand-new
results not yet revealed to the world. Brief descriptions of (hopefully)
all of the talks follow.
A. Gerasoulis described a general method for partitioning task
graphs and mapping tasks to processors. C. Kuzmaul of MasPar Corp.
discussed related issues, but from a different viewpoint.
Specific performance results for the Maspar
machine (running dense LU factorization) were provided by Rob Schreiber.
Methods for sparse matrix factorization on another "massively parallel"
machine (the Conection Machine) were presented by J. Gilbert (Xerox
PARC) and S. Kratzer (Supercomputing Research Center).
O. McBryan of Colorado Univ. presented performance measurements
for the Evans & Sutherland ES-1 and the Myrias SPS-2.
Several talks dealt with parallel methods for solving pde's.
S. McCormick (Univ. of Colorado) described an adaptive,
multilevel discretization method. S. Bowa also discussed
nonuniform grid generation, and focussed on domain decomposition
techniques. P. Frederickson of RIACS
explained how to parallelize the multigrid solver, giving
a "superconvergent" algorithm that runs on the
Connection Machine. M. London of Myrias Research Corp.
described his implementations of direct and iterative pde
solvers, which were developed for oil reservoir simulation.
D. Kincaid (U. Texas) described
ITPACKV, a new sparse-matrix software package for vector computers.
D. Bailey of NASA/Ames presented the "fractional Fourier transform,"
which generalizes the DFT to arbitrary resolution in frequency space,
and discussed parallel computations as well as applications for it.
O. Egecioglu (UC Santa Barbara) obtained good parallel speedup in computing
coefficients for rational interpolation.
F. Luk of Cornell showed how "algorithm-based fault tolerance" allows
us to check the output of a systolic array for arithmetic glitches;
he had been inspired by a previous Parallel Circus to work on this topic.
Several talks dealt with interesting applications for numerical computations.
J. Cavallaro of Rice Univ. is developing a systolic array for computing
the SVD, which will be used for robot control.
S. Barnard of SRI discussed the stereo image matching problem,
and a method named
Cyclops for solving it. D. Foulser of Yale gave an introduction to the
Human Genome Project, which endeavors to unravel the structure of human
DNA, and explained his algorithm for performing DNA sequence matching.
O. Tjorbjornsen of Univ. of Trondheim, Norway described
a new hardware/software system (using 80186s in a hypercube) for
database processing.
Tony Chan of UCLA discussed the philosophy of the physics of
parallel machines.
J. Barlow (Penn State) described an incremental conditional-number
estimator for sparse matrices.
Aside from the talks, which were very informal, the Circus provided the
opportunity for researchers to chat casually about the great issues of our time.
A reception at Gene Golub's house was a very enjoyable chance to
mingle, and the banquet at the Grand China restaurant was quite a treat!
The next Parallel Circus will take place Oct. 26 and 27, 1990,
in Toronto. Santa Barbara, CA was mentioned as a possible site for next Spring.
------------------------------
From: Jeffrey Kantor <jeff@iuvax.cs.indiana.edu>
Date: 22 Apr 90 15:57:14 GMT
Subject: Finite Element Mesh Generator in MATLAB
I've been putting together a set of MATLAB tools for constructing a mesh
of triangular finite elements with linear shape functions. It's primarily
intended for teaching. But some of the folks around here seem to think
it's pretty snappy.
The basic idea is that you can sit with your mouse and put together
a 2-D triangular mesh in a few minutes, accurately placing nodes and
wiring them together as elements. An existing mesh can be edited with the
mouse. The 'snap-to' grid can be used to zoom in on any portion of the
mesh. All of this is done is pure MATLAB, so that it should :-) be portable.
I'm doing this on a Mac, and testing on SparcStations.
Before I put to much more time it, though, I would like to know if there
are any other such MATLAB toolboxes out there. I don't want to reinvent
the wheel.
And I would also like to know if there is any general interest in such a
toolbox. Any input would be very much appreciated.
Jeff Kantor
Notre Dame
------------------------------
From: Alan Edelman <alan@math.mit.edu>
Date: Mon, 16 Apr 90 11:45:35 EDT
Subject: Large Dense Linear System Survey Report
LARGE DENSE LINEAR SYSTEM SURVEY REPORT
Some months ago, I asked in the NA digest who was solving large
dense systems of equations, why they were being solved, how big is n,
and for comments about accuracy. In fact, I only received ten
nearly complete responses and several other partial responses,
but all were quite interesting. Here I will report what
I have learned.
There are clearly more people involved in solving large dense
systems than those who generously took out the time to respond to me,
and I will mention some references given to me, which I myself have not
had the time to pursue. Furthermore, I suspect there may be uses in
economics, theoretical computer science, etc. but my inquiry never reached
people in these areas. Lastly, in this rapidly changing field there may
have been many new development since the time of my survey. In other
words, there is a lot of room for a more in depth study than what is given here.
Most responders are solving boundary integral equations arising
from elliptic PDE's in 3-space. Various buzz words used are
"boundary element methods," "method of moments," and "panel methods."
One specific application area mentioned a few times was radar cross
section analysis.
All, but two, main responses were from the US. The other two were
from Sweden and Switzerland. Some responders were at universities,
some from computer vendors, and others from the airline industry.
Clearly different people have different computing resources available.
I was not sure whether it was appropriate to preserve anonymity or
credit the respective researchers, and chose to err on the safe side
by not mentioning any particular names, companies, or institutions.
Only five responders said they are actually solving the equations
now. The responses were
1) 1000
2) 1026 but I know of people who have gone over 5000
3) the current upper limit in a reasonable length of time seems to be
somewhere between 20,000 and 40,000
4) 5000 (7000 is the probable maximum our system accepts)
5) 3000.
Thus the biggest number that I am aware of is 40,000.
Given faster computers and more memory people would like to
(Numbers 1 through 5 are from the same authors above, respectively.)
1) increase the size as much as possible
2) go higher than 1026 some day
3) have n as large as we can get it
4) (there is no need for more than 7000 for our present needs)
5) go higher
6) solve when n=20,000 to 100,000, and probably more for some applications
7) solve when n=20,000
8) solve a Helmholtz equation for n=100,000
9) solve for n=10,000
10) solve n=1,000,000.
Comments about accuracy (no particular order):
1) The desired accuracy is not clear. In the engineering community it
probably 2-3 digits. I want more to better understand the numerical method. 2) The methods are stable.
3) Most people, at least in the aerospace industry, use 64-bit precision,
... I have observed that there is a significant increase in usable
resolution over doing the same problems ... with 32-bit math.
By and large, we don't know how good our answers are. They seem to
be good enough for what we're doing, and certainly better than the
traditional methods of antenna engineering.
I think that our answers here ... are probably as good as you can get
with 64-bit machines ...
4) The kind of accuracy seems to be not very critical, ... for most practical
purposes, single precision arithmetic and up to five or four digits of
accuracy is sufficient.
5) The accuracy of the equation solver seldom causes any trouble.
There were almost no responses to my question about the condition
number of the problem.
General references listed were
1) "A survey of boundary integral equation methods for the numerical
solution of Laplace's Equation in three dimensions" by K.E. Atkinson
at the University of Iowa (paper)
2) "Field Computation by Moment Methods" by Roger Harrington
at Syracuse University. (book) (the "Bible" used by engineers)
3) Conference proceedings: "Topics in Boundary Element
Research" edited by C. Brebbia.
Other than the integral equation methods, some approximation
theorists are interested in large dense systems, but I am not aware
of anyone who is actually solving large dense systems today, sometimes
this is due to fears of highly ill-conditioned problems. Also
one person mentioned a large linear programming problem that was
800 by 12 million, where the 800x800 normal equations are formed and
solved.
The bottom line, so far as I can tell from the survey, is that
all large dense linear matrices being solved today more or less come
from the same types of methods. The largest system that has been solved has
n=40,000. No one mentioned anything precise about the accuracy they
were obtaining now or the conditioning of the problem, but most users
seemed more or less satisfied anyway.
*** I would like to thank everybody for their interesting responses.
If the information given here is incomplete, then at least this note
could be a first step towards more complete information.
*** I would like to continue to keep track of the current record
of the biggest dense system ever solved and would appreciate if anyone
knows or hears of n greater than 40,000 being solved to please let me know.
I will be happy to forward the largest to NANET, anonymously if requested.
Of course, any report of a large n should at least mention something about
accuracy.
Thanks again
Alan Edelman
CERFACS
Toulouse, France
na.edelman
------------------------------
From: Richard C. Allen <rcallen@cs.sandia.gov>
Date: Mon, 16 Apr 90 07:16:08 MDT
Subject: Fellowship in Computational Sciences at Sandia, Albquerque
RESEARCH FELLOWSHIP IN COMPUTATIONAL SCIENCES
Mathematics and Computational Science Department
Sandia National Laboratories
Albuquerque, New Mexico
Sandia National Laboratories invites applications and
nominations of outstanding your scientists for its 1990 Research
Fellowship in Computational Sciences.
The Sandia Research Fellowship will provide an exceptional
opportunity for young scientists who are performing leading-edge
research in the computational sciences. Sandia's Mathematics and
Computational Science Department maintains strong research
programs in theoretical computer science, analytical and
computational mathematics, computational physics and engineering,
advanced computational approaches for parallel computers,
graphics, and architectures and languages. Sandia provides a
unique parallel computing environment, including a 1024-processor
NCUBE 3200 hypercube, a 1024-processor NCUBE 6400 hypercube, a
Connection Machine-2, and several large Cray supercomputers. The
successful candidate must be a U.S. Citizen, must have earned a
recent doctorate in the sciences and should have made strong
contributions to numerical computation or computer science.
The fellowship appointment is for a period of one year, and
may be renewed for a second year. It includes a highly
competitive salary, moving expenses, and a generous professional
travel allowance. Applications from qualified candidates, or
nominations for the Fellowship, should be addressed to Robert H.
Banks, Division 3531-29, Albuquerque, NM 87185. Applications
should include a resume, a statement of research goals, and the
names of three references. The closing date for applications is
May 31, 1990. The position will commence during 1990.
EQUAL OPPORTUNITY EMPLOYER M/F/V/H
U.S. CITIZENSHIP IS REQUIRED
------------------------------
From: Pat Worley <worley@yhesun.EPM.ORNL.GOV>
Date: Tue, 17 Apr 90 14:38:29 EDT
Subject: PICL, a Portable Instrumented Communication Library
PICL, a portable instrumented communication library for multiprocessors,
is now available from netlib. PICL is a subroutine library that
implements a generic message-passing interface on a variety of
multiprocessors. Programs written using PICL routines instead of the
native commands for interprocessor communication are portable in the
sense that the source can be compiled on any machine on which the library
has been implemented. Correct execution is also a function of the
parameter values passed to the routines, but standard error trapping
is used to inform the user when a parameter value is not legal on a
particular machine. Programs written using PICL routines will also
produce timestamped trace data on interprocessor communication,
processor busy/idle times, and simple user-defined events if a few
additional statements are added to the source code. A separate facility
called ParaGraph can be used to view the trace data graphically.
The PICL source is currently written in C, but Fortran-to-C interface
routines are supplied on those machines where that is feasible.
To create PICL, you need picl.shar, port.shar, and the appropriate
machine-dependent code. Unshar all three in the same (empty) directory.
A README file describing how to create the library is bundled with the
machine-dependent shar file.
The picl subdirectory on netlib currently contains the following shar files:
picl.shar low-level PICL routines
port.shar high-level PICL routines
ipsc2.shar machine-dependent routines for the iPSC/2, including
FORTRAN-to-C interface routines
ipsc860.shar machine-dependent routines for the iPSC/860, including
FORTRAN-to-C interface routines
ncube.shar machine-dependent routines for the NCUBE/3200, but
without any FORTRAN-to-C interface routines
documentation.shar latex source of the working copy of the user
documentation. This will be issued as an ORNL
technical report.
Preliminary versions of PICL for the iPSC/1, the Cogent, the Symult S2010,
the Cosmic Environment, Linda, and Unix System V are also available.
Contact worley@msr.epm.ornl.gov for more information on these
implementations.
------------------------------
From: Robert Meyer <rrm@cs.wisc.edu>
Date: Tue, 17 Apr 90 15:31:22 -0500
Subject: Symposium on Parallel Optimization 2
SYMPOSIUM ON PARALLEL OPTIMIZATION 2
23 - 25 July 1990
Center for Parallel Optimization
Computer Sciences Department
University of Wisconsin
Madison, Wisconsin 53706
A 3-day symposium of invited presentations on
state-of-the-art algorithms and theory for the parallel solution
of optimization and related problems will be held at University
of Wisconsin at Madison with support from the AFOSR and in
cooperation with SIAM. (The SIAM National Meeting will be taking
place in Chicago the preceding week.) Emphasis will be on algorithms
implementable on parallel and vector architectures. Refereed
proceedings of the Symposium are planned as a special issue of
the new SIAM Journal on Optimization. Speakers include the following:
R. S. Barr, Southern Methodist University, Dallas
D. E. Brown, University of Virginia, Charlottesville
T. L. Cannon, Digital Equipment Corporation, Fairfax
R. De Leone, University of Wisconsin, Madison
J. E. Dennis, Rice University, Houston
L. C. W. Dixon, Hatfield Polytechnic, Hatfield
M. C. Ferris, University of Wisconsin, Madison
J. J. Grefenstette, Naval Research Laboratory, Washington
H. Muhlenbein, Gesellschaft fur Mathematik und Datenverarbeitung, S.Augustin
S. G. Nash, George Mason University, Fairfax
A. S. Nemirovsky, USSR Academy of Sciences, Moscow
Yu. E. Nestorov, USSR Academy of Sciences, Moscow
J. M. Ortega, University of Virginia, Charlottesville
K. Ritter, Technical University of Munich, Munich
J. B. Rosen, University of Minnesota, Minneapolis
R. Rushmeier, Rice University, Houston
A. Sameh, University of Illinois, Urbana
A. Sofer, George Mason University, Fairfax
P. Tseng, MIT, Cambridge
D. Van Gucht, Indiana University, Bloomington
L. T. Watson, VPI , Blacksburg
S. J. Wright, North Carolina State University, Raleigh
S. Zenios, University of Pennsylvania, Philadelphia
Although the symposium will be comprised of invited talks as
indicated above, registration (early registration by May 30: $50)
is open to all persons wishing to attend. A registration form and
information on lodging is deposited in netlib and may obtained via
email to netlib (mail netlib@research.att.com)
with the request:
send SPO from meetings
For information beyond that in netlib, contact the SPO2 Secretary,
Laura Cuccia, or one of the organizers, O. L. Mangasarian, R. R. Meyer
at the above address. Secretary: (608)262-0017,
email: laura@cs.wisc.edu, FAX (608)262-9777.
------------------------------
From: Gene H. Golub <golub@na-net.stanford.edu>
Date: Tue, 17 Apr 1990 23:01:29 PDT
Subject: New Additions to NA List
I've added quite a few names in the last few months. Here are the additions
and changes. I'm sorry to say we have no way to delete names now (!); we can
only add names.
Gene
IMACS: beauwens@BBRNSF11.bitnet
aboba: Bernard.Aboba@bmug.fidonet.org
academia_sinica: bmadis%beijing@ira.uka.de
agui: AGUI@EMDCCI11.BITNET
alefeld: AE02%DKAUNI2.bitnet@forsythe.stanford.edu
allen:rcallen@cs.sandia.gov
avila: avila@sjsumcs.mathcs.sjsu.edu
awatson: MA05@primea.dundee.ac.uk
axelsson: axelsson@scri1.scri.fsu.edu
babaoglu: numerica%dm.unibo.it@Forsythe.Stanford.EDU
baden: baden@csam.lbl.gov
batterson: sb@mathcs.emory.edu
beauwens: ulbg005@BBRNSF11.bitnet
bjorck: akbjo@math.liu.se
bjorksten: horus!alpha!jimb@isl.Stanford.EDU
block: IEBLOCK@wharton.upenn.edu
bogle: ucecb01@euclid.ucl.ac.uk
booth: A.S.Booth@durham.ac.uk
bratvold: bratvold@norunit.bitnet
brodzik: D5B5DA13079FC04C9E@vms.cis.pitt.edu
brueggemann: 211045%DHHDKRZ5.BITNET@Forsythe.Stanford.EDU
bstewart: billy@cscadm.ncsu.edu
butcher: butcher@maths.aukuni.ac.nz
cai: zcai@bnlux0.bnl.gov
callahan: ERVIN%morekypr.BITNET@Forsythe.Stanford.EDU
canning: fxc@risc.com
castro: castro@kodak.com
cerlpdr: CERLPDR%TECHNION.BITNET@Forsythe.Stanford.EDU
chun: chunj@ra.crd.ge.com
dee: SEODP%HDEDH1.BITNET@Forsythe.Stanford.edu
degroen:tena2!pieter@relay.EU.net
denham: zydeco@mathworks.com
deuflhard: deuflhard@sc.zib-berlin.dbp.de
dfausett: dfausett@zach.fit.edu
dhough: hough@ips.ethz.ch
doi: doi@IBL.CL.nec.co.jp
donato: donato@math.ucla.edu
egecioglu: omer@cs.ucsb.edu
einfeld: Einfeld@sc.zib-berlin.dbp.de
elliott: mt27amg@vm.tcs.tulane.edu
eydeland: alex@smectos.gang.umass.edu
fausett: dfausett@zach.fit.edu
fhanson: u12688@uicvm.cc.uic.edu
fletcher: fletcher@mcs.dund.ac.uk
fletcher: r.fletcher@primea.dundee.ac.uk
flores: JFLORES@CHARLIE.USD.EDU
garratt: tjg%maths.bath.ac.uk@NSFnet-Relay.AC.UK
geller: a84687%tansei.cc.u-tokyo.ac.jp
gersztenkorn: zaxg04@gpsb.trc.amoco.com
goldberg: goldberg@parc.xerox.com
goldfarb: goldfarb@cunixd.cc.columbia.edu
grace: andy@mathworks.com
greenberg: greenber@titan1.math.umbc.edu
greenstadt:greensta@sjsumcs.SJSU.edu
griewank: griewank@antares.mcs.anl.gov
gropp: gropp@antares.mcs.anl.gov
grote: grote@CGEUGE11.bitnet
haber:hendrix@Sun.COM
hanson: hanson%imsl.uucp@uunet.uu.net
harvard: na-list@mgh.harvard.edu
hasegawa: hasegawa@fuis.fuis.fukui-u.ac.jp
hasson: mhasson@copper.colorado.edu
heinreichsberger: heinreich@EVEV88.una.at
herbin: raphaele@masg1.epfl.ch
hmarshall: idaho@caen.engin.umich.edu
hodel: S_HODEL@ducvax.auburn.edu
hull: tehull@na.toronto.edu
ikebe: ikebe@gama.is.tsukuba.ac.jp
iserles: ai%camnum@atmos-dynamics.damtp.cambridge.ac.uk
jea: fjut006%twnmoe10.bitnet@forsythe.stanford.edu
jeltsch: jeltsch@math.ethz.ch
jennings: munnari!madvax.maths.uwa.oz.au!les@uunet.UU.NET
jimack: MTHPJK@VAXA.Heriot-Watt.Ac.UK
jjuang: JJUANG%TWNCTU01.BITNET@Forsythe.Stanford.EDU
jmarshall: mv10801@uc.msc.umn.edu
jmorris: jmorris@mcs.dund.ac.uk
jouvelot: jouvelot@ensmp.fr
kahaner:kahaner@xroads.cc.u-tokyo.ac.jp
kamath: kamath@vino.enet.dec.com
kanada: kanada@tansei.cc.u-tokyo.ac.jp
kearfott: rbk@usl.edu
kershaw: maa013@central1.lancaster.ac.uk
koshy: KOSHY@msg.UCSF.EDU
kriegsmann: G_KRIEGSMANN@nuacc.acns.nwu.edu
kstewart: stewart@sdsu.edu
kuo: cckuo%portia.usc.edu@usc.edu
lai: chenlai%mtha.usc.edu@usc.edu
levesley: mty012@cck.coventry.ac.uk
leyk: leyk@macomb.tn.cornell.edu
lfausett: lfausett@zach.fit.edu
liebling: LIEBLING@ELMA.EPFL.CH
lindquist: lindquis@ams.sunysb.edu
little: jnl@mathworks.com
lwatson: na.watson@na-net.stanford.edu
maechler: maechler@stat.washington.edu
math_sinica: math@twnas886.bitnet
mathias: mathias@patience.stanford.edu
mcelwee: mcelwee@cup.portal.com
mcenery: SCMP6012%IRUCCVAX.UCC.IE@Forsythe.Stanford.edu
meir: AMEIR@ducvax.auburn.edu
mit: NUMANAL@NERUS.PFC.MIT.EDU
mitchell: wmitchell@atl.ge.com
nanderson: anderson@vino.enet.dec.com
niethammer: AF01@DKAUNI2.bitnet
orel: bojan.orel%uni-lj.ac.mail.yu@relay.cs.net
osborne: mro250@csc2.anu.OZ.au
oser: jpbm@athena.umd.edu
osterman: osterman@cmcl2.NYU.EDU
otoole: jotoole@relay.nswc.navy.mil
overton: overton@cs.nyu.edu
papamichael: Nicholas.Papamichael%brunel.ac.uk@NSFnet-Relay.AC.UK
parady: garth!apd!bodo@apple.com
patricio: FCMTJJJ@civc2.rccn.pt
pchin: pchin@watfun.waterloo.edu.
pernice: usimap@sneffels.utah.edu
peterson: tep@mssun7.msi.cornell.edu
petiton: petiton@cs.yale.edu
pitsianis: schin@ibm.com
ptang: tang@mcs.anl.gov
ringertz: ht_rzu@ffa1.sunet.se
roberson: kyle%phoebus.hydro.pnl.gov@pnlg.pnl.gov
robin: robinf@etca.etca.fr
rothblum: rothblum@cancer.bitnet
rump: rump@tuhhco.rz.tu-harburg.de
rwright: wright@uvm.edu
saad: saad@hydra.riacs.edu
saied: saied@cs.uiuc.edu
sanz-serna: sanzserna@cpd.uva.es
saylor: saylor@inf.ethz.ch
scales: zjas23@trc.amoco.com
schlick: SCHLICK@ACF1.NYU.EDU
schumitzky: aschumitzky@gamera.usc.edu
seneta: seneta_e@maths.su.oz.au
shirakawa: shirakaw@ka.tsukuba.ac.jp
shoaff: wds@zach.fit.edu
shure: loren@mathworks.com
sli: sli@cs.purdue.edu
smale: smale@cartan.berkeley.edu
spaeht: 040624%DOLUNI1.BITNET@Forsythe.Stanford.edu
springer: springer-07@DCFCM5.DAS.NET
stenger: stenger@cs.utah.edu
tanabe: tanabe@sun312.ism.ac.jp
tanner: NA%AECLCR.BITNET@Forsythe.Stanford.EDU
tli: li@nsf1.mth.msu.edu
tuminaro: tuminaro@cs.sandia.gov
werner: or470@dbnuor1.bitnet
widlund: widlund@math.berkeley.edu
wimp: wimpjet@DUVM.bitnet
woltring: ELERCAMA@HEITUE5.bitnet
yun: dyun@wiliki.eng.hawaii.edu
zarantonello: sergioz@fai.fai.com
zha: zha@na-net.stanford.edu
zhang: zhang@umiacs.UMD.EDU
------------------------------
End of NA Digest
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