URL for the World Wide Web:
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From: W. Kahan <wkahan@EECS.Berkeley.EDU>
Date: Sat, 17 Mar 2001 16:45:20 -0800 (PST)
Subject: Quadratic Matrix Equation
> From the NA Digest Vol. 01 No. 10 of 10 March 2001
> From: Matthew Brand <brand@merl.com>
> Date: Mon, 5 Mar 2001 20:05:06 -0500 (EST)
> Subject: Quadratic Matrix Equations
> I'm trying to solve a matrix equation X'*A*X+B*X+C=0 with all matrices
> square and A,C positive definite. I'm aware of generalized eigenmethods
> for matrix quadratic equations and Schur forms for Riccati equations, but
> don't see a way to massage this problem into either of those forms.
Response:
Brand's problem has a "closed form" solution of sorts, but
complicated by the ambiguous nature of the solutions X ; there
may be many of them, perhaps infinitely many, or none at all.
The data given are square matrices A, B and W of which A = A'
and W = W' are symmetric and positive definite. (Brand's C
has been replaced by W so that symmetric letters can be used to
represent symmetric matrices.) Desired is a solution X of the
equation
X'AX + BX + W = O .
Presumably (though Brand does not say so) all matrices are
real. Here is a way to compute such solutions X as exist:
First, perhaps by using Matlab's chol(...) operation, perform
the Cholesky factorization of A = R'R to get an upper triangle
R . This is feasible because A is positive definite. Then set
E := BR**-1 ( = B/R in Matlab's notation), and compute a
symmetric matrix H := (E**-1)W(E**-1)' ( = E\W/E' in Matlab).
Roundoff may obscure the symmetry of H , so overwrite it by
H := (H + H')/2 . The eigendecomposition of H (matlab's eig) is
a factorization H = QVQ' in which V is real diagonal and Q real
orthogonal; Q' = Q**-1 . The equation T**2 + T + V = O can now
be solved elementwise for a real diagonal T provided no diagonal
element of V exceeds 1/4 . If diagonal elements of V are not
all distinct then there are infinitely many non-diagonal solutions
T too. For each solution T compute (usually symmetric) Y := QTQ'
and then X := (R**-1)YE' (= R\Y*E' ) turns out to be one of the
desired solutions of Brand's equation.
There are many ways for the foregoing formulas to go wrong because
of roundoff, but that is a story for another day.
W. Kahan
------------------------------
From: Tim Davis <davis@cise.ufl.edu>
Date: Wed, 14 Mar 2001 18:01:35 -0500
Subject: UMFPACK, Software for Unsymmetric MultiFrontal Method
UMFPACK Version 3.0Beta is available at
http://www.cise.ufl.edu/research/sparse
UMFPACK is a set of routines for solving unsymmetric sparse linear systems,
Ax=b, using the Unsymmetric MultiFrontal method. It is written in ANSI/ISO C,
with a Matlab (Version 6.0) interface. UMFPACK relies on the Level-3 Basic
Linear Algebra Subprograms (dense matrix multiply) for its performance.
The code also has a C-callable interface. It's been ported to Sun Solaris,
SGI Irix, Linux, and Windows NT.
It finds a column-preordering that reduces fill-in, with a modified version of
COLAMD (type "help colamd" in Matlab V6.0). Next, the method breaks the
factorization of the matrix A down into a sequence of dense rectangular frontal
matrices. The frontal matrices are related to each other by a supernodal
column elimination tree, in which each node in the tree represents one frontal
matrix. This analysis phase also determines upper bounds on the memory usage,
the floating-point operation count, and the number of nonzeros in the LU
factors. This is a major departure from the "on-the-fly" pivot search of
UMFPACK V2, which can lead to erratic fill-in and provides no a priori bounds.
With the perspective of the analysis phase, any candidate pivot column in the
frontal matrix is identical (in terms of nonzero pattern), and so is any row.
However, the (right-looking) numerical factorization phase has more information
than the analysis phase. It keeps track of approximate row and column degrees,
and can re-order columns within a front to reduce fill, and can select pivot
rows based on sparsity-preserving criteria as well as numerical considerations
(relaxed threshold partial pivoting).
The easiest way to use UMFPACK is within Matlab. For example, assuming you
have Matlab V6.0 and install UMFPACK:
UMFPACK: | Matlab approximate equivalent:
---------------------------------------------------------------------
x = umfpack (A, '\', b) ; | x = A \ b
|
x = umfpack (b, '/', A) ; | x = b / A
|
[L,U,P,Q] = umfpack (A) ; | Q = colamd (A) ;
| [L,U,P] = lu (A (:,Q)) ;
|
[Q,F,C] = umfpack (A, 'symbolic') ; | Q = colamd (A) ;
| [count,h,parent,post] = ...
| symbfact (A (:,Q), 'col') ;
If you give it a try on other systems, let me know how the installation goes,
and I'll incorporate any changes in the final V3.0 release.
------------------------------
From: Zhaojun Bai <bai@cs.ucdavis.edu>
Date: Tue, 13 Mar 2001 11:13:08 -0800 (PST)
Subject: Symposium at Stanford on Iterative Methods for Matrix Problems
Dear Colleagues,
We are organizing a one day symposium on iterative methods for matrix
problems on Friday May 4, 2001, following the Preconditioning 2001
Conference at Lake Tahoe. The symposium will be held at Stanford University.
If you would like to attend and speak please let us know asap. If you
want to speak, please send a title and an abstract to bai@cs.ucdavis.edu.
We welcome all our colleagues to attend the event.
Gene Golub (Stanford University) and
Zhaojun Bai (University of California, Davis)
------------------------------
From: Serhiy Shtovba <serg@faksu.vstu.vinnica.ua>
Date: Mon, 12 Mar 2001 09:20:35 +0200
Subject: Conference in Ukraine on Measurement and Control
FIRST CALL FOR PAPERS: MCCS-2001
The Sixth International Conference
"MEASUREMENT AND CONTROL IN COMPLEX SYSTEMS"
Vinnitsa State Technical University, Vinnitsa, Ukraine
October 8-12, 2001
http://www.vstu.vinnica.ua/mccs2001 (after March 12, 2001)
Abstract Submission Deadline: April 10, 2001
Organized by VINNITSA STATE TECHNICAL UNIVERSITY
in cooperation with
- Institute of Electrical Engineering and Electronics (IEEE);
- System Analysis Institute of the Ukraine Academia of Science
and of Ministry of Education and Science of Ukraine;
- Lviv National Technical University "Lvivska Politechnica", Ukraine;
- SPA "Systema", Lviv, Ukraine.
OBJECTIVES
The goal of this conference is the meeting of the specialists in the field
of control and management of technical, ecological, managerial and economic,
medical and biological and other complex systems in order to find common
approaches, to exchange ideas, to discuss tendencies of development of this
particular scientific sphere, to establish fruitful relations and to
accustom talented young researches to scientific search. Special attention
is going to be paid to the use of mathematical modeling, the optimization
and other scientific approaches of technical sciences to the solving the
problems of environment protection, sustainable use of natural resources,
management, health etc.
TOPICS
The technical issues to be addressed include, but not limited to:
Mathematical modeling of complex systems:
- information systems;
- managerial and economic systems;
- technological processes;
- power systems;
- environment;
- medical and biological systems;
- based on computational intelligence;
Prospective technical tools of measurement and control:
- meteorological providing of measuring;
- primary measuring transducers;
- communication tools;
- information protection;
- signal processing;
- information display;
- means of regulation;
Control in
- power engineering;
- environment protection;
- medical and biological systems;
- managerial and economic systems;
- technological processes;
Complex systems optimization:
- CAD of control systems;
- optimization of non-linear complex systems;
- adaptive complex systems;
- multicriterial optimization.
CONFERENCE ORGANIZERS
General Chair - Academic Boris Mokin - rector of Vinnitsa State Technical
University, Ukraine.
Local Organizing Chair - Dr. Vitaliy Hrabko - the first vice-rector of
Vinnitsa State Technical University, Ukraine.
CONFERENCE SITE
The MCCS-2001 will take place in Vinnitsa City.
FURTHER INFORMATION
Please send the all messages regarding MCCS-2001 to:
Dr.Sc., Prof., Vladimir Dubovoy,
Head of Computer Control Systems Department,
Vinnitsa State Technical University,
Khmelnitskoe Shosse, 95,
21021, Vinnitsa, Ukraine
dub@faksu.vstu.vinnica.ua
------------------------------
From: Elliot Tonkes <ejt@maths.uq.edu.au>
Date: Mon, 12 Mar 2001 17:24:33 +1000 (EST)
Subject: Conference in Brisbane on Computational Techniques
CONFERENCE ANNOUNCEMENT
CTAC 2001
University of Queensland, Brisbane
Australia
16-18 July 2001
INVITATION FOR PARTICIPATION AND REQUEST FOR ABSTRACTS
The 10th Biennial Computational Techniques and Applications, CTAC01
will be held at the University of Queensland over July 16-18, 2001.
An introduction barbeque will be held on the evening of Sunday July 15.
Participation is invited from any aspects of computational mathematics
and scientific computing. The conference proceedings will be
electronically published in the ANZIAM Journal (Electronic supplement).
Invited speakers are:
* Professor Hans-Georg Bock (Interdisciplinary Center for
Scientific Computing (IWR), Heidelberg, Germany)
* Professor Lothar Reichel (Kent State University, Ohio, USA)
* Professor Carl Chiarella (School of Finance and Economics,
University of Technology, Sydney, Australia)
* Professor Graeme Fairweather (Mathematical and Computer Sciences,
Colorado School of Mines, Golden, USA)
* Professor Hugh Possingham (Mathematics and Zoology, University of
Queensland, Brisbane, Australia)
The conference web page is at http://conference.maths.uq.edu.au/ctac2001.
On-line registration, abstract submission and full paper submission is
available via the web site.
Requests for information should be sent to Professor Kevin Burrage,
Department of Mathematics, University of Queensland,
or by email to kb@maths.uq.edu.au.
------------------------------
From: Donald Estep <estep@math.colostate.edu>
Date: Mon, 12 Mar 2001 04:34:54 -0700
Subject: Workshop on the Preservation of Stability under Discretization
Call for Participation
Workshop on the Preservation of Stability under Discretization
Wednesday, May 30 -- Saturday, June 2
Colorado State University
Fort Collins, CO
Organizers: Donald Estep and Simon Tavener
Stability is a term used to describe a wide variety of issues revolving
around the physical observability of a solution of a differential
equation. Stability lies at the very heart of the ability to make
predictions about physical situations from mathematics and is
particularly relevant when numerical approximation is involved, since
discretization causes perturbation of both the model and the data.
Numerical stability issues are typically complex because addressing such
questions often requires a wide range of mathematical techniques,
involving not only standard methods of numerical analysis, but ideas
from dynamical systems, geometry, functional analysis, and the theory of
differential equations. This raises barriers both to young researchers
trying to learn about numerical stability and to communication between
researchers working in different areas yet facing similar stability problems.
The goal of the Workshop on the Preservation of Stability under
Discretization is twofold: (1) to increase the accessibility of
numerical stability issues for young researchers and (2) provide an
opportunity for the exchange of information and ideas between
specialists in different application areas. The Workshop will host a
series of lectures by leading experts, each of whom will each address a
separate aspect of stability under discretization. The lectures will be
aimed towards an audience of advanced graduate students and non-
specialists. In addition, the invited speakers will host a series of
discussion and analysis sessions for students and young researchers and
there will be a daily session of contributed talks.
The following invited speakers have confirmed their participation
M. Ablowitz, U. Colorado at Boulder
B. Cockburn, U. Minnesota
L. Dieci, Georgia Tech
M. Gunzburger, Iowa State
A. Iserles, Cambridge U.
H. Keller, Caltech
S. Larsson, Chalmers U. Technology
C.-W. Shu, Brown U.
A. Spence, U. Bath
In addition,
R. Scott, U. Chicago
A. Stuart, U. Warwick
are possible speakers, among others.
We will be able to provide partial support for travel expenses for
a number of students and young researchers interested in participating
in the Workshop. Funds are being provided by the National Science
Foundation and Colorado State University.
People interested in participating should contact
Don Estep (estep@math.colostate.edu)
or
Simon Tavener (tavener@math.colostate.edu)
Best regards,
Don Estep and Simon Tavener
------------------------------
From: Suter Bruce W Civ AFRL/IFGC <Bruce.Suter@rl.af.mil>
Date: Mon, 12 Mar 2001 10:52:38 -0500
Subject: Conference in Crete on Multirate Systems and Wavelets
WSES/IEEE MULTIRATE SYSTEMS and WAVELET ANALYSIS 2001
(organized by Prof. Bruce Suter )
Location: Rethymnon, CRETE (GREECE).
JULY 8-15, 2001
http://www.softlab.ntua.gr/~mastor/Neural2001.htm
ALL THE ACCEPTED PAPERS will be published:
1)in the CD-ROM Proceedings (with Search Facilities and Page Numbering)
as well as
2)in the Electrical and Computer Engineering International Reference
Book Series of WSES PRESS as Post-Conference Books (Hard cover, velvet
paper, international circulation).
These will be different International Editions (with different ISBN).
This material will be ready at the opening of the Multiconference and
will be distributed to the participants.
EXTENSION OF THE DEADLINE FOR PAPER SUBMISSION
UNTIL MARCH 20, 2001
TOPICS:
Multirate Systems and Filter Banks
Filter Bank Design
Multirate Filter Design
Joint Time-Frequency Analysis
Wavelet Transforms
Wavelets and Subband Coding
Controller synthesis methods for sampled-data systems
Multirate systems design
Multirate systems for pattern recognition
Multirate systems for Multimedia and Video technologies
Robustness of sampled-data systems
Novel Filter Banks
Multiscale Feature Detection
Multirate and Wavelet Applications
Multirate systems in radar application and relevant problems
Wavelet Analysis in Artificial Vision
Wavelets and Artificial Intelligence
Wavelets and Neural Networks
Wavelets and Fuzzy Logic
Wavelets and Evolutionary Programming Techniques
Mathematical Wavelet Analysis
Algebraic Problems for Wavelets
Communications Signal Processing, including Image and Video Processing
and Compression
Biomedical Signal Processing, including EKG Processing and Compression
Hardware Design Technology, including A/D and D/A Converters and
Fourier Transform Processors
Education in Wavelets and Multirate Systems
Any relevant problem, new technique, new methodology, new application in
Multirate Systems and Wavelets
------------------------------
From: Saleet Jafri <jafri@utdallas.edu>
Date: Mon, 12 Mar 2001 16:53:54 -0600
Subject: Conference in Dallas on Mathematical and Computational Biology
Frontiers in Mathematical and Computational Biology
June 17-19, 2001
UT Dallas, Richardson, TX
http://www.utdallas.edu/~darcy/CONF/2001/compbio.html
Travel Funds are available for graduate students from the mathematical,
physical and chemical sciences departments.
Deadlines
TRAVEL AWARDS application deadline: April 27
(Travel Funds are available for graduate students from the mathematical,
physical and chemical sciences departments)
Abstract deadline: April 27.
Early Registration deadline: May 11.
Sponsors
University of Texas at Dallas,
Program in Mathematics and Molecular Biology (PMMB),
Bionumerik Pharmaceuticals
Workshop Topics
I. Neuroscience
II. Cardiac Dynamics
III. Biochemical Reaction Networks and Cell Signaling
IV. Bioinformatics and Functional Genomics
V. DNA Energetics
Invited Speakers
Craig Benham (Mount Sinai School of Medicine),
Lee Bulla (U. T. Dallas),
Saleet Jafri (U. T. Dallas),
John Lederer, (U. of Maryland),
Yoram Rudy (Case Western Reserve),
Irwin Tobias (Rutgers),
Dan Tranchina (New York University),
Eric Young (Johns Hopkins),
John Wagner (U. of Connecticut Health Center),
Tandy Warnow (UT Austin)
Organizers
Saleet Jafri (chair), UT Dallas; Barbara Shipman (co-chair), UT
Arlington; Isabel Darcy (co-chair), UT Dallas
Information
http://www.utdallas.edu/~darcy/CONF/2001/compbio.html
------------------------------
From: Luca Pavarino <Luca.Pavarino@mat.unimi.it>
Date: Sat, 17 Mar 2001 07:35:44 +0100 (MET)
Subject: Workshop in Zurich on Domain Decomposition Methods
Two-day workshop on
DOMAIN DECOMPOSITION METHODS
June 7-8, 2001
ETH Zurich, Switzerland.
Sponsors
Department of Mathematics, University of Milan (www.mat.unimi.it)
Seminar for Applied Mathematics, ETH Zurich (www.sam.math.ethz.ch)
Organizers: L. Pavarino, University of Milan
Ch. Schwab, ETH Zurich
A. Toselli, ETH Zurich
O. Widlund, Courant Institute
The following speakers have confirmed their participation:
Y. Achdou (Paris VII)
A. Alonso (University of Milan)
Ch. Bernardi (Universite Pierre et Marie Curie, Paris)
A. Buffa (Istituto di Analisi Numerica, Pavia)
M. Dryja (Warsaw University)
V. Heuveline (University of Heidelberg)
R. Hoppe (University of Augsburg)
A. Klawonn (GMD, St. Augustine)
C. Lasser (Technical University of Munchen)
Y. Maday (Universite Pierre et Marie Curie, Paris)
F. Nataf (Ecole Polythecnique, Paris)
A. Patra (SUNY, Buffalo)
L. Pavarino (University of Milan)
A. Quarteroni (EPFL and Politecnico di Milano)
F. Rapetti (Laboratoires ASCI, Paris)
A. Valli (University of Trento)
O. Widlund (Courant Institute, New York)
B. Wohlmuth (University of Augsburg)
The main purpose of this workshop is to give an overview of some of
the most recent developments in the field of Domain Decomposition.
We understand Domain Decomposition in a broad sense as relating to
the construction of preconditioners for the large algebraic systems
of equations which often arise in applications, by solving smaller
instances of the same problem. We also, most certainly, wish to
include studies of methods built from different discretizations in
different subdomains such as in multi-physics models, mortar finite
elements, etc. The workshop will also allow the participants to meet
informally and give opportunities for people to make new acquaintances.
If you are interested in participating please contact the organizers.
For further information, such as program, hotel, and travel
information, please see
http://www.sam.math.ethz.ch/~toselli/DDW2001/main.html
------------------------------
From: Heinrich Voss <voss@tu-harburg.de>
Date: Mon, 12 Mar 2001 13:37:49 +0100
Subject: Visiting Faculty Position in Hamburg-Harburg
Visiting Professor of Applied Mathematics
at the Technical University Hamburg-Harburg
The Technical University Hamburg-Harburg invites applications
for a visiting professorship of applied mathematics in the
International Bachelor Programme in General Engineering Science
starting October 1, 2001 for one year with the possibility of extension.
Preference is given to candidates with a strong background in partial
differential equations and applications in engineering sciences.
However, candidates who have demonstrated exceptional abilities in other
areas of research in applied mathematics and have a personal commitment
to excellence in teaching are also encouraged to apply.
The visitor will join the section of mathematics which maintains
research programmes in scientific computing with applications in
structural dynamics and chemical engineering. She or he will have
to teach both, a course in linear algebra or calculus in the
international bachelor's programme, and a graduate course.
The language of instruction is English.
Applicants are expected to be native speakers and to hold a
Ph.D. degree in mathematics or applied mathematics. Applications
containing a statement of interest, curriculum vitae, and names,
addresses and e-mail addresses of referees should be submitted to the
President of the Technical University Hamburg-Harburg
Prof. Dr.-Ing. Christian Nedess
D-21071 Hamburg
Germany
Applications must be received by April 30, 2001. Questions about the
position may be directed to Prof. Heinrich Voss by telephone
(+49 40 7718 3279), electronic mail (voss@tu-harburg.de) or by FAX
(+49 40 7718 2696).
------------------------------
From: Kontoghiorghes Erricos <Erricos.Kontoghiorghes@unine.ch>
Date: Sun, 11 Mar 2001 12:05:54 +0100
Subject: Research Assistantship Position in Switzerland
PhD fellowship
Applications are invited for a Ph.D. studentship (research assistantship)
in the Department of Computer Science, University of Neuchatel and
ETHZ, Switzerland.
The project aims to extend recent research in the development of
parallel algorithms and efficient numerical tools for solving
large-scale linear model estimation problems. Applicants should be
able to demonstrate good knowledge in (Parallel) Computing and
Numerical Linear Algebra. The working language will be English.
The net monthly salary after all taxes is approximately (2200 Swiss
Francs) and teaching assistantship may be available for supplementary
income (+1500 Swiss Francs). For the teaching assistantship knowledge
of French is required. The position is available immediately.
Requests for further details and applications in the form of CV (plain
text sent by e-mail - NO word docs) should be directed to:
Erricos J. Kontoghiorghes <erricos.kontoghiorghes@unine.ch>
and
Peter Arbenz <arbenz@inf.ethz.ch>
Erricos John Kontoghiorghes
Institut d'informatique, Universite de Neuchatel,
Rue Emile-Argand 11, Case Postale 2,
CH-2007 Neuchatel, Switzerland
------------------------------
From: Daniel Pierce <Daniel.Pierce@PSS.Boeing.com>
Date: Fri, 16 Mar 2001 12:23:06 -0800
Subject: Staff Positions at Boeing
The Mathematics and Engineering Analysis group at Boeing has immediate
openings in the areas of Computational Science and Applied Linear Algebra.
The successful Computational Science candidate will minimally
have: a masters level competency in numerical analysis and applied
mathematics; a thorough understanding of one or more of the
following computing languages: Fortran, Fortran90, C, or C++;
a good understanding of a wide range of computing environments
(both platforms: Sun, SGI, Cray, PC, etc. and operating systems:
UNIX, Linux, Windows, etc.); the ability to work well in a group as
well as independently; good communication skills, and the desire
to learn more mathematics and to see it successfully deployed on
real applications.
Knowledge of Java and/or experience using the web as an interface
into other tools would be a plus.
Job responsibilities include: software maintenance i.e.: porting,
debugging, and consultation; integration of computational tools into
packages such as Excel and Matlab; and math algorithm implementation,
certification and documentation. Possible mathematical areas supported
include optimization, linear algebra, integral and differential equations,
approximation theory, and parallel computing.
The successful Applied Linear Algebra candidate will minimally have:
an in depth knowledge of applied linear algebra, demonstrated ability to
do independent research, ability to work very well on a team as well as
independently and very strong communication skills. In addition the
successful candidate would have a demonstrated ability to program in
Fortran, Fortran90, C or C++. A Ph.D. in applied mathematics with a
specialization in applied linear algebra would be expected. A Ph.D. in
computer Science would be considered if the emphasis area was still
linear algebra.
Job responsibilities include: To perform applied research in applied linear
algebra addressing Boeing problems. Areas of research possibilities include
linear system solves (direct or iterative), eigenproblem solutions, and matrix
analysis for large sparse matrix problems, model order reduction, solution of
matrix equations, updating and downdating factors and solutions, very large
structured matrix problems, new matrix factorizations, etc. Emphasis of
research would be on algorithm development and practical solution
development. The successful candidate will have work opportunities on
a huge range of applications including: structural analysis, signal processing,
control, optimal design, optimal manufacturing, operations research, data
mining, options pricing, communications, security, etc. Other mathematical
areas in our organization that require linear algebraic support include
optimization, operations research, probability and statistics, approximation
theory and geometry, ordinary and partial differential and
differential algebraic equations, integral equations and parallel computing.
The Mathematics and Engineering Analysis organization is part
of the Boeing research and development organization. We are located
in Bellevue, WA a suburb of Seattle. Besides doing applied R&D, the
group provides software and consultation in the design, manufacture and
support of Boeing products. These include commercial jet transports,
military aircraft and missiles, and space vehicles and systems. The
successful candidate will be a part of a diverse group of nearly 100 people
providing mathematical support and solutions to the entire Boeing Company.
The opportunity to be a part of defining the future of aerospace travel,
as an applied mathematician, is real and exists everyday in our
organization. Please send a resume in ASCII or MS Word format to
daniel.j.pierce@boeing.com
Boeing is an affirmative action/equal opportunity employer
------------------------------
From: Technical Group <journal@dodo.inm.ras.ru>
Date: Tue, 13 Mar 2001 15:06:00 +0300 (MSK)
Subject: Contents, East-West Journal of Numerical Mathematics
EAST-WEST JOURNAL OF NUMERICAL MATHEMATICS
Vol.9, No.1, 2001, pp.1-76
CONTENTS
Anisotropic mesh adaptation technique
for viscous flow simulation
V.Dolejsi
pp.1-24
H-matrix approximation for elliptic solution operators
in cylinder domains
I.P.Gavrilyuk, W.Hackbusch, and B.N.Khoromskij
pp.25-58
Analysis of the streamline-diffusion finite element method
on a piecewise uniform mesh for a convection-diffusion
problem with exponential layers
M.Stynes and L.Tobiska
pp.59-76
------------------------------
End of NA Digest
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