NA Digest Sunday, August 22, 1993 Volume 93 : Issue 31

Today's Editor:

Cleve Moler
The MathWorks, Inc.

Submissions for NA Digest:

Mail to

Information about NA-NET:

Mail to


From: Alan Edelman <edelman@BOURBAKI.MIT.EDU>
Date: Mon, 16 Aug 93 17:19:21 EDT
Subject: New Address for Alan Edelman

New Address for Alan Edelman

Alan Edelman
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139
Office Phone: (617) 253-7770
Home Phone: (617) 566-3688


From: Alan Craig <>
Date: Sun, 22 Aug 93 09:06:25 +0100 (BST)
Subject: Change of Address for Alan Craig

As from 1st September my new address will be

Alan Craig
Domaine de Voluceau
BP 105
78153 Le Chesnay Cedex

email to Durham will still find me.



From: Gene Golub <golub@sccm.Stanford.EDU>
Date: Sat, 21 Aug 93 10:40:41 PDT
Subject: SIAM Conferences

I recently attended the Third SIAM Conference on Linear Algebra Signals,
Systems and Control in Seattle. Several persons made comments to me which I
think should be discussed publicly. Perhaps in light of these comments, it is
necessary to re-think the SIAM policy on conferences. Other
organizations, please note.

Here are some of those comments.
1) There are too many parallel sessions with too few attendees.
2) Talks were rehashs of talks given in the previous two years.
3) At least one session was dedicated to a commercial product: Matlab.
4) The meeting began too early in the morning, 8am.
5) This conference was organized by the same person who organized the
previous ones.
6) Many talks had little to do with the main theme of the meeting.

Perhaps the policy of accepting all abstracts and parallel sessions is
now out of date.

If you wish to make your comments known to the SIAM leadership, send a
message to na.siam.

Gene Golub


From: Giuseppe Paruolo <AGG0@ICINECA.CINECA.IT>
Date: Tue, 17 Aug 93 09:16:32 +0000 (SET)
Subject: How to Discriminate Between Typing Mistakes and Intentional Ones?

Problem: a numeric code of about 11 digits must be specified in certain
documents; some of the digits depends on the others, so it is
possible to detect any mistake; since it is possible to extract a
sample of the incorrect documents and perform a manual search to
determine the correct codes, now the problem is to discriminate
between typing mistakes and intentionally deceptive mistakes.
Question: what is needed is a routine/algorithm/method, possibly certified
or previously used in significant cases (or at least some pointer
to the right place where to ask), aimed to discriminate between
small errors - probably due to typing mistakes - and other kind of
changes, subject to be investigated as deceptive actions.
Thank you in advance.

Giuseppe Paruolo - CINECA Supercomputing Center - Bologna, Italy


From: Paul Nevai <>
Date: Tue, 17 Aug 1993 05:29:57 -0400 (AST)
Subject: Query on Convergence of Infinite Products of Matrices

We (Walter Van Assche and Paul Nevai) are interested in the convergence of
the infinite product $\prod (I+A_n)$ where $I$ is the identity matrix and
$A_n$'s are square matrices (of fixed finite order). We know that the
infinite sums $\sum A_n$ (conditionally, elementwise) and $\sum ||A_n||^2$
(the square of the norms) converge. The matrices $A_n$ do not commute with
each other. Under what (additional, if any) conditions can we conclude that
$\prod A_n$ converges? Can you give me some references or suggestions who I
should contact on such matters? Thanks...Paul Nevai

P.S. We would be interested even in the case when the matrices are $2x2$
and the diagonal elements are always zero.

Paul Nevai
Department of Mathematics
The Ohio State University nevai@ohstpy.bitnet
231 West Eighteenth Avenue 1-614-292-3317 (Office)
Columbus, Ohio 43210-1174 1-614-292-5310 (Answering Machine)
The United States of America 1-614-292-1479 (Math Dept Fax)


From: D.J. Evans <>
Date: Tues, 17th Aug 93
Subject: Software Package PARASPAR

I should like to obtain details about the software package PARASPAR.
Can anyone supply me with further information.

Prof. D.J. Evans
Parallel Algorithms Research Centre (PARC)
Loughborough University
Leics. LE11 3TU, U.K.

FAX: 0509-211586.


From: Choi-Hong Lai <>
Date: Tue, 17 Aug 93 12:37:23 +0100 (BST)
Subject: Anonymous FTP at Greenwich

Anonymous FTP at the University of Greenwich:

We have recently fixed our ftp facility. Therefore it is possible for you to
obtain nma series by anonymous ftp to and the nma series are
recorded as .dvi files under the directory pub/nma. A readme file in pub/nma
gives a brief description. This readme file will be updated from time to time
as more reports are included into the series.

A large number of people response to my previous message regarding the
report nma001. I have sent off the tex file via email to some of the people
before the ftp was fixed. Hardcopies were sent off to those who have
specifically asked for. I apologise for not sending hardcopy to everyone.

Choi-Hong Lai

University of Greenwich
School of Math Stat & Comp
Wellington Street
London SE18 6PF


From: Jalel Rejeb <>
Date: Tue, 17 Aug 93 18:56:12 EDT
Subject: Nonlinear Elliptic PDE and Picard Iteration

We are trying to solve nonlinear elliptic equations of the form:

Uxx + Uyy = f(U,x,y)

Where f is nonlinear function of U. We need to solve for U(X,Y) in rectangular
region and the boundary are of mixed type.
We wish to solve this problem using point iteration method , known
also as Picard Method. That is assume U = U(k-1) on the right side of Eq.1
during the k th iteration, until U(k) = U(K-1). So iterate the
following linear equation until convergence:

Uxx(k) + Uyy(k) = f(U(k-1),x,y)

OUR question is there any way we can improve the accuracy and
convergence of the point iteration method. We are obtaining results that
are ok but!, but not as accurate as Newton Method ...

Any advises and suggestions (or where should we look) are appreciated.



From: Richard Franke <0083P%NAVPGS.BITNET@cmsa.Berkeley.EDU>
Date: Thu, 19 Aug 93 10:42:27 PDT
Subject: Numerical Solution of an Integral-differential Equation

An engineering colleague recently asked about methods for solving a
particular kind of integral-differential equation. I'm passing it
on the the Digest. The equation is of the form
f(x) = g(x) + | h(x-y) f"(y) dy
If anyone can give any pointers to the literature, or other help,
I'm sure he would appreciate it. A response can be made directly
to me at Thanks.


From: Stefan Vandewalle <>
Date: Wed, 18 Aug 93 11:25:24 +0200
Subject: New Book on Parallel Multigrid Waveform Relaxation

I would like to announce the publication of the book:

"Parallel Multigrid Waveform Relaxation for Parabolic Problems"
by Stefan Vandewalle, in the series Teubner-Skripten zur Numerik,
B.G. Teubner Stuttgart, Germany, 1993.
(16.2 x 23.5 cm, 247 pages, DM 39.80, ISBN 3-519-02717-8)


Waveform relaxation is a highly parallel iterative method for
solving very large systems of ordinary differential equations.
Over the years this method has been applied almost exclusively
for the systems that model VLSI electronic circuits.

In the present work the author studies waveform relaxation
methods for parabolic partial differential equations of initial
boundary-value and time-periodic type. It is shown both theoretically
and by numerical experimentation that waveform relaxation, when
accelerated by using multigrid, is a highly effective algorithm.
It combines a low serial complexity with a high parallel efficiency
and it is easily vectorisable.

The book starts with an introductory overview of the waveform relaxation
theory and practice, and provides an in-depth analysis of multigrid
waveform relaxation. It discusses the parallel implementation of
classical time-stepping schemes and analyses the computational
complexity of waveform relaxation methods. A large number of case-
studies illustrate the performance of the methods for linear and
nonlinear problems.


From: Tom Franklin <>
Date: Mon, 16 Aug 93 16:30:55 +0100 (BST)
Subject: Symposium on Parallel Numerical mathematics

Symposium on
Parallel Numerical Mathematics

Sponsored by
The Centre for Novel Computing
University of Manchester
Manchester Centre for Computational Mathematics

In conjunction with
The London Mathematical Society

To be held at
Department of Computer Science
Manchester University

9th and 10th September 1993

Nick J Higham
A Parallel Algorithm for Computing the Polar Decomposition

Bo Kagstrom
Design, Modelling and Evaluation of Shared Memory and Distributed Memory

Danny C Sorensen
Implicitly Restarted Arnoldi Methods for Large Scale Eigenvalue Problems

Ken McKinnon
Dynamic Programming on Distributed memory MIMD machines.

Virginia Torczon
Parallel Pattern Search Methods for Unconstrained Optimization

Salvatore Filippone
Numerical algorithms on distributed memory architectures.

Eric Grosse
Domain decomposition on an FDDI network

Ian Gladwell
Parallel Algorithms for Functional Equations

Petter Bjorstad

Guy Lonsdale
Migrating Industrial Crash-simulation Software

Full details available by anonymous ftp from (
in pub/nareps/Parallel_Symposim.93


Tom Franklin
Centre for Novel Computing Phone +44 61 275 6134
Department of Computer Science Fax +44 61 275 6204
University of Manchester
Manchester email
M13 9PL


From: John Belward <>
Date: Wed, 18 Aug 93 10:25:45 EST
Subject: Post Doctoral Position at The University of Queensland

High Performance Computing Unit

Post Doctoral Research Fellow

The University of Queensland is seeking a PostDoctoral Research
Fellow for it's recently established High Performance Computing Unit.
The Unit has a 4096 processor Maspar and will have Cray Y-MP
supercomputer installed by September 1 next.

The functions of the Unit are
to encourage multidisciplinary projects in the
area of High Performance Computing

to provide research into High Performance Computing methodologies

to initiate and provide support for High Performance Computing
applications in industry, commerce and research.

Applicants should have experience with vector architectures, knowledge
and expertise in MIMD and/or distributed configurations and research
interests in Computational Mathematics.
The research program for the unit will include collaborative work
with the Queensland Department of Primary Industries.
The successful appointee will work closely with The Department of
Mathematics Scientific Computing Group.

The appointment will be for a period of 18 months in the first instance.

Further details can be obtained from Professor Kevin Burrage.
Addresses are: e-mail
fax Int + 61 7 3651477
Postal address
Department of Mathematics
The University of Queensland
Queensland 4072


From: Gene Golub <golub@sccm.Stanford.EDU>
Date: Sun, 22 Aug 93 13:48:28 PDT
Subject: Post-Doc Position at Stanford

We are seeking a person who has a doctorate in the mathematical or
engineering sciences who has an interest in the development of
numerical algorithms, especially linear algebra applications to signal
processing. Applicants should be available as of Oct 1, 1993 or soon
thereafter. Persons interested should send a copy of their CV and
relevant papers to Gene Golub. Post-doc positions of this nature have
been previously held by such persons as Paul Vandooren, George
Cybenko, Bart De Moor and Kjell Gustafsson.

Gene Golub

Gene Golub, Fletcher Jones Professor of Computer Science
Director, Scientific Computing/ Computational Math
Office: Margaret Jacks Hall, Room 306
Office Phone: 415/723-3124 Home Phone: 415/323-0105
Office FAX : 415/723-2411 Home FAX : 415/323-0105


From: Jorge More <>
Date: Wed, 18 Aug 1993 15:32:55 -0500
Subject: Research Position at Argonne National Laboratory

Research Position
Mathematics and Computer Science Division
Argonne National Laboratory

Argonne National Laboratory invites outstanding candidates to
apply for a research position in the Mathematics and Computer
Science Division. Candidates should have a Ph.D. in applied
mathematics, computer science, or a related field and at least
three years of research experience.

The division has strong research programs in scientific computing,
linear algebra, optimization, partial differential equations, and
computer science areas such as software tools for parallel computing,
scalable I/O, and advanced scientific visualization. We seek a
candidate with a research agenda to augment these programs in
addition to a strong interest in the development of state-of-the-art
numerical methods for solving computational science problems.

The Mathematics and Computer Science Division supports an excellent
computational environment that includes high-performance scientific
workstations, a scientific visualization laboratory, and state-of-the-art
parallel computers (including the IBM SP-1 and access to the Intel
Touchstone DELTA).

Applications should be addressed to Walter McFall, Box mcs-108450,
Employment and Placement, Argonne National Laboratory,
9700 S. Cass Avenue, Argonne, IL 60439, and must include a
resume' and the names and addresses of three references.
For further information, contact Jorge More' or Rick L. Stevens
(; 708-252-7162).

Argonne is an affirmative action/equal opportunity employer.


From: Richard Sincovec <sincovec@sirius.EPM.ORNL.GOV>
Date: Fri, 20 Aug 93 16:31:08 -0400
Subject: SAC '94 Special Track on Scientific Computing

Call For Papers

March 6-8, 1994
Phoenix Civic Plaza, Phoenix, Arizona


SAC'94 is the annual conference of the ACM Special Interest
Group on Applied Computing (SIGAPP). For the past eight
years, SAC's have been a primary forum for applied computing
practitioners and researchers. Again this year, SAC'94 will
be held in conjunction with the 1994 ACM Computer Science
Conference in Phoenix. State-of-the-Art and State-of-the-
Practice papers in all areas of applied computing are

Special track on Scientific Computing (SC)

A special track on Scientific Computing will be held in SAC'
94. It will be a forum for engineers, researchers and prac-
titioners throughout the world to share technical ideas and
experiences relating to implementation and application of
Scientific Computing. Original papers and tutorial (half or
full day) and panel proposals are invited in all areas of SC
applications. Major topics of interest include but are not
limited to the following:

Agronomy Aerospace & Aviation
Animal Science Biochemistry
Biology (except Biomedical) Botany
Chemistry Engineering (all areas)
Entomology Forestry
Geography Horticulture
Microbiology Petrochemicals
Petroleum Engineering Physics
Physiology Psychology
Technology Transfer Zoology

Scientific Computing Track Advisory Committee

Ken Barker University of Manitoba (CA)
Hossein Hakimzadeh Indiana University
Ramzi Haraty The Aerospace Corporation
Sushil Jajodia George Mason University
Ken Nygard North Dakota State University
Richard F. Sincovec Oak Ridge National Laboratory
Bhavani Thuraisingham The MITRE Corporation
LiQuan Qi University of New South Wales (AU)
Andy Walker Nottingham University (UK)
Lonny Winrich University of North Dakota
Cui-Qing Yang University of North Texas
Osman Yasar University of Wisconsin-Madison

Guidelines For Submission

Original papers from the above-mentioned areas will be con-
sidered. Accepted articles will be published in the SAC'94
Conference Proceedings to be published by the ACM Press.
Best student papers will qualify for awards. Expanded ver-
sions of selected papers from all categories will be con-
sidered for publication in the ACM/SIGAPP quarterly APPLIED

In order to facilitate the blind external review process,
submission guidelines must be strictly adhered to:

o Submit 6 copies of manuscript to the SAC'94 Scientific
Computing track chair at the address below.

o Author name(s) and address(es) are NOT to appear in the
body of the paper, and self-reference should be in
third person.

o Body of paper should not exceed 5,000 words (approx. 20
pages, double-spaced).

o Separate cover sheet should be attached to each copy,
containing (1) title, (2) author(s) and affiliation(s),
and (3) address (including e-mail and fax number) to
which correspondence should be addressed.

o In order to qualify as a student paper, ALL authors
must be students at the time the manuscript was submit-

o All papers and panel proposals must be submitted by
September 1, 1993.

SAC'94 Co-Sponsoring SIGs

SIGAPL (APL), SIGAPP (Applied Computing), SIGBIT (Business
Information Technology), SIGBIO (Biomedical Computing),
SIGCUE (Computer Uses in Education), SIGFORTH (FORTH) and
SIGSMALL/PC (Small and Personal Computing Systems and Appli-

Direct Correspondence, Inquiries And Submissions Relating To
This Special Track To:

Mahir S. Ali
(SAC94 Scientific Computing Track Chair)
Department of Computer Science
University of North Dakota
P.O. Box 9015
Garnd Forks, ND 58202-9015
Tel: (701) 777-4107
Fax: (701) 777-3330



For General Inquires Contact The Conference Director:

Ed Deaton
Dept. of Mathematical Sciences
San Diego State University
San Diego, CA 92182
Tel: +1 619 594 5962
Fax: +1 619 594 6746


From: Gene Golub <golub@sccm.Stanford.EDU>
Date: Sat, 21 Aug 93 13:12:34 PDT
Subject: Stanford Reports

The following Stanford reports are available, on a limited basis, in
hard copy. Please send a message to my secretary, Beverly Harlan,
( giving your postal address.

Gene Golub

Manuscript NA-92-05, May 1992
Adaptive Chebyshev Iterative Methods for Nonsymmetric Linear Systems
Based on Modified Moments, by D. Calvetti, G.H. Golub, and L. Reichel.

Manuscript NA-92-06, July 1992
Fast Iterative Solution of Stabilized Stokes Systems; Part II: Using
Block Preconditioners, by David Silvester and Andrew Wathen.

Manuscript NA-92-07, August 1992
The Periodic Schur Decomposition. Algorithms and Applicationsk, by
A. Bojanczyk, G.H. Golub, and P. Van Dooren.

Manuscript NA-92-08, August 1992
A Domain Decomposition Approach to Solving the Helmholtz Equation with
a Radiation
Boundary Condition, by Oliver Ernst and Gene H. Golub.

Manuscript NA-92-09, August 1992
An Implementation of a Generalized Lanczos Procedure for Structural
Dynamic Analysis on Distributed Memory Computers, by David R. Mackay
and Kincho H. Law.

Manuscript NA-92-10, August 1992
A Parallel Row-Oriented sparse Solution Method for Finite Element
Structural Analysis, by Kincho H. Law and David R. Mackay.

Manuscript NA-92-11, September 1992
A New Approach For Solving Perturbed Symmetric Eigenvalue Problems,
by Cheryl Carey, Hsin-Chu Chen, Gene Golub, and Ahmed Sameh.

Manuscript NA-92-12, September 1992
Matrix shapes invariant under the symmetric QR algorithm, by Peter
Arbenz and Gene H. Golub.

Manuscript NA-92-13, September 1992
The canonical correlations of matrix pairs and their numerical
computation, by Gene H. Golub and Hongyuan Zha.

Manuscript NA-92-14, September 1992
Cyclic reduction/multigrid, by Gene H. Golub and Ray S. Tuminaro.

Manuscript NA-92-15, October 1992
Fast solution of the Helmholtz equation with radiation condition by
imbedding, by Oliver Ernst

Manuscript NA-92-16, November 1992
Model problems in numerical stability theory for initial value
problems, by A.M. Stuart and A.R. Humphries.

Manuscript NA-92-17, November 1992
Runge-Kutta methods for dissipative and gradient dynamical systems,
by A.R. Humphries and A.M. Stuart.

Manuscript NA-92-18, November 1992
An analysis of local error control for dissipative, contractive and
gradient dynamical systems, by A.M. Stuart and A.R. Humphries.

Manuscript NA-92-19, December 1992
Eulerian number asymptotics from a recursion equation, by E. Giladi
and J.B. Keller.

Manuscript NA-92-20, December 1992
Use of linear algebra kernels to build an efficient finite element
solver, by Howard C. Elman and Dennis K.Y. Lee.

Manuscript NA-92-21, December 1992
On the error computation for polynomial based iteration methods, by B.
Fischer and G.H. Golub.

Manuscript NA-93-01, May 1993
Fifth Annual Affiliates Meeting, May 7, 1993, sponsored by Scientific
Computing and Computational Mathematics Program.

Manuscript NA-93-02, June 1993
Inexact and preconditioned Uzawa algorithms for saddle point problems,
by Howard C. Elman and Gene H. Golub.

Manuscript NA-93-03, June 1993
A Lanczos-based method for structural dynamic re-analysis problems,
by Cheryl M. M. Carey, Gene H. Golub, and Kincho H. Law.

Manuscript NA-93-04, July 1993
A multishift QR iteration without computation of the shifts,
by Augustin A. Dubrulle and Gene H. Golub.


From: Richard Brualdi <>
Date: Tue, 17 Aug 1993 07:02:25 -0500 (CDT)
Subject: Special Issue of LAA Honoring J. J. Seidel

Linear Algebra and its Applications
Special Issue in Honor of J. J. Seidel

We are pleased to announce a special issue of LAA in honor of J. J. Seidel
in recognition of his many important and elegant contributions to the
interplay between linear algebra and combinatorics and geometry.
Papers are invited concerning any aspect of linear algebra and its
applications, in particular, its application to combinatorics and geometry.
All contributions will be subject to the normal reviewing process. The
deadline for submissions is August 30, 1994.

Submissions should be sent to one of the special editors of this issue:

Aart Blokhuis
Department of Mathematics and Computer Science
Technical University of Eindhoven
P.O. Box 513
5600 MB Eindhoven, The Netherlands


Willem H. Haemers
Department of Econometrics
Tilburg University
P.O. Box 90153
5000 LE Tilburg, The Netherlands


Alan J. Hoffman
Department of Mathematical Sciences
IBM Research Division
T. J. Watson Research Center
P.O. Box 218
Yorktown Heights, NY 10598.


Papers can also be sent to the editor-in-chief:

Richard A. Brualdi
Department of Mathematics
University of Wisconsin
480 Lincoln Drive
Madison, WI 53706.


We invite you to join in honoring our esteemed colleague.


From: Ralph B Kearfott <>
Date: Sun, 22 Aug 1993 03:36:48 -0500
Subject: Student Edition of Interval Computations


Announcing special
of the International

Guest editors:
Guenther Mayer and Vladik Kreinovich

The future of Interval Computations is with the students researchers
entering the field. Their vision, their insights, their approaches
will shape the future research. To highlight their
contributions, the Editorial Board of the Interval Computations
Journal decided to make a special issue that will contain
high-quality papers written by students (either alone, or in co-authorship with
their professors). These papers will undergo the same refereeing as
all the other papers. We will try our best to publish this issue as fast
as possible.

Papers authored or co-authored by students will be automatically
entered into a Best Paper contest. The Editorial Board of the Interval
Computations Journal will choose the
winning paper. The student author of the best paper will be
given a special certificate and a free one-year subscription to
Interval Computations.

Papers should be written in any version of TeX (preferably AMS-TeX).
Please submit your papers to

Vladik Kreinovich
Department of Computer Science
University of Texas at El Paso
El Paso, TX 79968
phone (915) 747-6951
fax (915) 747-5030

Deadline for abstracts: December 1, 1993
Deadline for papers: March 1, 1994


From: SIAM <tate@siam.ora>
Date: Fri, 20 Aug 93 08:31:33 EST
Subject: Contents: SIAM Numerical Analysis

SIAM Journal on Numerical Analysis, v.30, no.6

Domain Decomposition Type Iterative Techniques for Parabolic Problems on
Locally Refined Grids
Richard E. Ewing, Raytcho D. Lazarov, Joseph E. Pasciak, Panayot S. Vassilevsky

A Quasi-Monte Carlo Approach to Particle Simulation of the Heat Equation
William J. Morokoff and Russel E. Caflisch

Estimation of Variable Coefficients in the Fokker-Planck Equations Using Moving
Node Finite Elements
H.T. Banks, H.T. Tran, and D.E. Woodward

On the Question of Turbulence Modeling by Approximate Inertial Manifolds and
the Nonlinear Galerkin Method
John G. Heywood and Rolf Rannacher

The Global Dynamics of Discrete Semilinear Parabolic Equations
C.M. Elliott and A.M. Stuart

A New Scheme for the Approximation of Advection-Diffusion Equations by
Daniele Funaro

Numerical Methods for the Simulation of Flow in Root-Soil Systems
Todd Arbogast, Mandri Obeyesekere, and Mary F. Wheeler

Solution of Nonlinear Diffusion Problems by Linear Approximation Schemes
J. Kacur, A. Handlovicova, and M. Kacurova

Application of Global Methods in Parallel Shooting
M.E. Kramer and R.M.M. Mattheij

FFT-Based Preconditioners for Teoplitz-Block Least Squares Problems
Raymond H. Chan, James G. Nagy, and Robert J. Plemmons

Quadrature Methods for Strongly Elliptic Equations of Negative Order on Smooth
Closed Curves
J. Saranen and L. Schroderus

Optimal A-Poseriori Parameter Choice for Tikhonov Regularization for Solving
Nonlinear Ill-posed Problems
O. Scherzer, H.W. Engl, and K. Kunisch


From: Carlos Moura <>
Date: Fri, 20 Aug 93 17:36:47 EST
Subject: Contents: Computational and Appllied Mathematics

(Matematica Aplicada e Computacional)
Vol. 11, Issue 3, 1992

Dongwoo SHEEN
A numerical method for approximating wave propagation in a porous medium
saturated by a two-phase fluid

On the global convergence of a curvilinear search method for unconstrained

Nordsieck forms of stiffly-stable Adams-type cyclic methods that are
insensitive to step-size changes

Carlos HUMES Jr.
A projection-feasible direction method for continuous capacity flow

Differentiable dependence on data and optimal control of a Muskat problem
for imminscible fluids in porous media

Oscar H. BUSTOS and Alejandro C. FREY


End of NA Digest