NA Digest Sunday, July 11, 1993 Volume 93 : Issue 25

Today's Editor:

Cleve Moler
The MathWorks, Inc.

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From: Gene Golub <golub@sccm.Stanford.EDU>
Date: Thu, 8 Jul 93 22:04:19 PDT
Subject: Alston Householder

Alston Householder died od a massive stroke on Sun, Jul 4. He was 89
years old. Those of us who attended the Householder meeting at Lake
Arrowhead were fortunate to see him before he passed away.

Householder made many contributions to linear algebra and numerical
analysis. Many techniques that we use so easily were originated by
him. But beyond his technical skill, he was a kind and gentle soul. He
was modest and being in his presence was uplifting. He never
denigrated others.

Letters of condolence can be sent to his widow, Heidi Householder, 6235
Tapia drive, Malibu, CA 90265 or his son, Dr. John Householder, 743
North A Street, Oxnard, CA 93030. If you prefer, send an e-mail to me
and I will send copies to Heidi and John. ( There is a surviving
daughter but I do not know her address; she lives in Britain).

We will organize a memorial fund at a later date.



From: Mustafa Pinar <>
Date: Mon, 5 Jul 93 10:14:28 CET
Subject: A Latex Question

I have the following question for Latex experts:

I have a number of abstracts that I am trying to put
together in a booklet. This can be done using the

include or input

commands. However, I would like to produce a table
of contents with the correct page numbers at the
beginning. But Latex requires -- to my knowledge --
that each separate file is treated as a section or
a chapter to include it in the table of contents.
I do not want to number each abstract. Is anybody
familiar with a way to do this? I would appreciate any help.

Mustafa Pinar
Institute for Numerical Analysis


From: Manuel Galan Moreno <>
Date: Mon, 5 Jul 93 16:09:53 +0100
Subject: Information about GMRES Algorithm

I would appreciate any information about papers or books
on Y. Saad's GMRES(k) algorithm for solving linear systems.
Also any information on vector/parallel implementations.

Manuel Galan


From: W. E. Schiesser <WES1@SSCVX1.SSC.GOV>
Date: Mon, 5 Jul 1993 14:25:40 -0500 (CDT)
Subject: Programs from Book by Silebi and Schiesser

The programs in the book

"Dynamic Modeling of Transport Process Systems"
C. A. Silebi and W. E. Schiesser
Academic Press, San Diego, 1992

including the programs for the problems at the ends of the chapters, are
available on a 3.5 inch, DOS-formatted diskette. The programs generally
implement numerical solutions to ODEs and PDEs as applied to problems in
engineering and the physical sciences, particularly the dynamics of momentum,
heat and mass transfer and reaction kinetics. Requests can be sent to:

W. E. Schiesser

(until August 22, 1993):
SSC Laboratory, MS4003
Accelerator Division
2550 Beckleymeade Avenue
Dallas, TX 75237

(214) 708-3525 (phone)
(214) 708-4804 (fax) (Internet)

(after August 25, 1993):
Lehigh University
Iacocca Hall, Room D307
111 Research Drive
Bethlehem, PA 18015 USA

(215) 758-4264 (office)
(215) 758-5057 (fax)
(215) 758-5297 (fax) (Internet)


From: Uri Ascher <>
Date: 5 Jul 93 13:01 -0700
Subject: COLDAE Available from NETLIB

The code COLDAE is now available from netlib. (Say "send coldae from ode"
in your e-mail message to netlib in order to get it.) This code, written
by Ray Spiteri and myself, is an extension of the fortran code
COLSYS/COLNEW. It attempts to solve multipoint boundary value systems of
semi-explicit differential-algebraic equations of index at most 2 (this
includes fully implicit index-1 daes and boundary value odes as special
cases). It uses projected collocation at Gaussian points and does
automatic mesh selection and error control of the differential solution
components. A paper describing the various techniques involved will
appear some day in SIAM's SISC.


Uri Ascher


From: Tim Davis <>
Date: Tue, 6 Jul 93 11:15:17 -0400
Subject: UMFPACK: General Unsymmetric Sparse Matrix Solver

UMFPACK: Unsymmetric-pattern MultiFrontal Package

The Unsymmetric-pattern MultiFrontal Package (UMFPACK) solves Ax=b using LU
factorization, where A is a general unsymmetric sparse matrix. The method
relies on dense matrix kernels (the BLAS) to factorize rectangular frontal
matrices, which are dense submatrices of the sparse matrix being factorized.
UMFPACK is available via netlib ("send umfpack.shar from misc") or anonymous
ftp ( Both single- and double-precision ANSI
Fortran-77 versions are included. UMFPACK is freely available for research
purposes. For commercial use, please contact Tim Davis.

In one of our extensions to the method, we are investigating a distributed
memory, factor-only version that would be used to factor a sequence of matrices
that have an identical sparsity pattern. In order to evaluate the performance
and effectiveness of these extensions, we are in search of realistic test
problems that produce sequences of matrices with identical and unsymmetric
sparsity patterns. Matrices of order greater than 1000 are of most interest.
If you have or know of such test problems, please contact Tim Davis
( or Steve Hadfield (

Tim Davis, Computer and Info. Sci. Dept., Univ. of Florida, Gainesville, FL.
Joint work with Iain Duff, Rutherford Appleton Laboratory, England, and
CERFACS, Toulouse, France.


From: Kelly Black <>
Date: Mon, 5 Jul 93 09:26:47 -0400
Subject: Spectral Multi-Domain Methods Workshop

Preliminary Summary for Spectral Multi-Domain Methods Workshop
May 16-18, 1994
Center for Research in Scientific Computing
North Carolina State University
Raleigh, North Carolina, USA

Topic: Interface conditions for spectral multi-domain methods. There
is an intricate balance between what happens at the interfaces and the
trade-offs between the discretization and the actual implementation.
This is further compounded when considering different computational
architectures. The topics are not limited to these concerns and may
also include topics that reflect the interests of the speakers. Our
primary interest is to provide a forum for attendees to freely
exchange ideas with a view to collaboration.

Format: We anticipate each speaker providing an introductory lecture
and a lecture on their area of expertise. The introductory lectures
can be coordinated so that topics central to spectral multi-domain
techniques are covered. Presentations are limited to the invited
speakers; however, there will be a poster session. Also, the number
of attendees will be limited in the interest of providing a more
intimate setting.

Organizing committee:
Kelly Black North Carolina State University
Wei Cai University of North Carolina, Charlotte
Jeffrey S. Scroggs North Carolina State University

Scientific committee:
H.T. Banks North Carolina State University
Paul Fischer Brown University

List of speakers (tentative):
Paul Fischer Brown University
Daniele Funaro Universita di Pavia
David Gottlieb Brown University
George Karniadakis Princeton University
Steven Orszag Princeton University

For more information, please contact
Kelly Black
Center for Research in Scientific Computing
Box 8205, North Carolina State University
Raleigh, North Carolina, 27695-8205, USA


From: Stephen Vavasis <>
Date: Wed, 7 Jul 93 14:12:41 -0400
Subject: 12th Householder Symposium

The 12th Householder Symposium on Numerical Algebra was held in Lake
Arrowhead, California during the week of June 14. The Householder
Symposium, which was formerly known as the Gatlinburg Conference, was
renamed in 1990 in honor of Alston S. Householder and is held once
every three years. Householder, who attended the 1993 meeting,
organized four Gatlinburg Conferences at the beginning the series and
is known for his pioneering work in numerical linear algebra. Gene
Golub recently reported the sad news that Householder passed away in

The meeting, which was organized by Tony Chan of UCLA and Gene Golub
of Stanford, was the largest ever in the series, with approximately
160 participants. It has been traditional to hold the meeting in an
isolated venue--Lake Arrowhead is located in the mountains 60 miles
east of Los Angeles--in order to promote informal interaction. The
meeting was funded in part by the National Science Foundation and The
Mathworks, Inc. Babette Dalton of UCLA helped organize much of the
logistics of the meeting.

Highlighting the 1993 meeting was the presentation of two Householder
awards for the best PhD dissertation in numerical linear algebra
during the past three years. The two winners were Barry Smith and
Hong-Guo Xu. Smith, who received his PhD in mathematics from the
Courant Institute of New York University in 1990, has worked in the
area of domain decomposition and finite element methods. Domain
decomposition refers to a class of numerical methods for solving
boundary value problems by solving independent problems on subdomains
and then numerically iterating to obtain a global solution. Smith's
dissertation, which was advised by Olof Widlund, contains new, optimal
results on convergence rates for domain decomposition applied to
problems where the subdomains do not have significant overlap and
where the coefficients are varying.

Smith was the Wilkinson Fellow at Argonne National Laboratory
following the awarding of his PhD, and is currently in the mathematics
department of UCLA.

Xu received his PhD in mathematics from Fudan University, Shanghai, in
1991. His dissertation, which was advised by Jiang Er-xiong, focuses
on numerical solution of the Riccati equations. In his thesis, he
derived structured algorithms for the solution of both continuous time
and discrete time algebraic Riccati equations. These algorithms are
based on a simple but elegant proof of the existence of particular
square roots of matrices with Hamiltonian or symplectic structure. Xu
derived an error analysis and showed how to use iterative refinement
for ill-conditioned Riccati equations. He also conducted thorough
testing of the new algorithms to verify theoretical error bounds. Xu
is currently in the mathematics department of Fudan University.

Beresford Parlett, speaking for the Householder award committee, said
that the criteria were mathematical innovation, computational
experiments, and applicability of the results. The committee also
decided to select one nominee, Ali Sayed, for a special mention.
Sayed received his PhD in August of 1992 in electrical engineering
under the direction of Thomas Kailath. His dissertation describes how
a variant of Gaussian elimination can be applied to a variety of
problems in linear algebra and control theory, including Toeplitz
systems and Pade tables, to yield efficient algorithms. The key
concept in the dissertation is a generalization of "low displacement
rank." Sayed's work unifies many previous and seemingly complicated
algorithms in the literature. Sayed is headed for the electrical
engineering department of UCSB.

The bulk of the meeting was 30 plenary lectures spread over five days.
The lectures covered various topics of current interest, including
parallel linear algebra, sparse systems, boundary value problems,
updating and downdating factorizations, perturbation bounds, and
structured systems. Many of the talks described applications of
linear algebra, including applications to partial differential
equations and signal and image processing. In addition to the plenary
lectures, there were concurrent sessions in the evenings on topics
such as parallel computation, multigrid and domain decomposition
methods, eigenvalue algorithms, and others.

The meeting opened with plenary talks by Paul Van Dooren, Hong-yuan
Zha and Sabine Van Huffel on matrix factorizations arising in signal
processing and statistics. Van Dooren spoke on numerically stable
simultaneous factorization of a product of matrices arising in
control. Algorithms for canonical correlations arising in statistics
was the subject of Zha's presentation. Van Huffel compared structured
total least squares to constrained total least squares, and applied
them to biomedical problems.

A sequence of talks by James Demmel, Roy Mathias, and Nick Higham
focused on the relationship between parallelism and numerical
stability in linear algebra. Demmel described an eigenvalue toolkit
using new algorithms based on the matrix sign function. The method,
though ideal for parallelism, has weaker stability properties compared
to traditional sequential methods. Mathias showed that computing
signatures by parallel prefix methods was less stable than traditional
accumulation. Parallel triangular solvers were the subject of Nick
Higham's talk; he showed that several proposed algorithms are not as
stable as sequential back-substitution.

Two speakers addressed sparse matrix methods. John Gilbert described
implementation and experimentation with geometric mesh partitioning,
important for parallel iterative methods and sparse Gaussian
elimination in finite element problems. Stan Eisenstat described new
approaches to sparse unsymmetric factorization that attempt to
incorporate successful ideas from symmetric algorithms.

Several talks focused on iterative algorithms for solving nonsymmetric
and indefinite linear systems. Gerald Sleijpen showed how to prevent
stagnation in the BiCGSTAB iterative algorithm in an extension denoted
BiCGSTAB(l). Anne Greenbaum described a new analysis of the GMRES
algorithm that can better distinguish matrices for which the method
will converge quickly. Michael Saunders compared two iterative
methods, LSQR and Craig's method, showing equivalence in some cases.

Boundary value problems were the subject of three talks. Steve
Vavasis proposed new elimination methods for solving boundary value
problems that are guaranteed to be numerically stable in the presence
of wild variation in the coefficient field. Andy Wathen proposed new
preconditioned iterative methods for Stokes' flow with optimal bounds
on the condition number. Coincidentally, both of these speakers
analyzed properties of the symmetric indefinite linear system
[H, A' ; A, 0]
to obtain their results. Hans Munthe-Kaas showed how to unify various
fast Poisson solvers in terms of abelian groups.

A number of talks focused on updating, downdating, and rank-detection
algorithms. These algorithms are very important in signal processing,
where it is necessary to maintain information such as numerical rank
for a time-varying signal. In a time-varying signal, "old"
information must somehow be eliminated from the factorization and rank
approximations as time passes. C.-T. Pan spoke on recent progress in
rank-revealing QR factorization, which is used as an efficient
substitute for the full singular-value decomposition. Haesun Park
spoke on a hybrid, more stable method for downdating the URV
decomposition, also used for monitoring numerical rank. Ming Gu
proposed new algorithms for downdating the singular-value
decomposition itself. Frank Luk derived a new factorization of matrix
pairs amenable to updating.

Chris Paige delivered the banquet plenary address on the history of
the C-S decomposition and angles between subspaces. His talk showed a
history going back to Jordan, and focused on recent contributions by
C. Davis, W. Kahan and G. W. Stewart.

Perturbation theory was the subject of several talks. Michael Overton
discussed a new way to analyze stability in Hamiltonian systems; the
stability issue can be expressed as an eigenvalue perturbation
problem. Ji-guang Sun gave new backwards-perturbation estimates for a
wide variety of least-squares and eigenvalue problems that are the
best possible estimates in many cases. Ilse Ipsen showed a new method
for analyzing a variety of eigenvalue perturbation problems; her
method is based on writing additive perturbations as matrix
multiplications. Nick Trefethen presented experimental comparisons
between how perturbations of the coefficients affect the zeros of a
polynomial, and how perturbations of a companion matrix affect its
eigenvalues. The results seem to be very similar, but only if
"balancing" is used on the companion matrix.

Three speakers addressed ill-posed problems. Jay Kuo discussed the
use of wavelets in image compression and processing. Bob Plemmons
described new preconditioners for iterative methods used in image
recovery. Per Christian Hansen discussed a new analysis for
determining when and how conjugate gradient can reveal a regularized
solution for ill-posed problems.

Three talks focused on analysis of structured problems. Zdenek
Strakos spoke on the relation between numerical errors in Gaussian
quadrature computation and the Lanczos iteration. Roland Freund spoke
on stabilizing "fast" algorithms (that is, O(n^2) flops) for Toeplitz
systems using look-ahead procedures. Martin Gutknecht described new
"superfast" algorithms (that is, O(n (log n)^2) flops) for the same

Leslie Foster in his talk gave examples arising in differential and
integral equations for which Gaussian elimination with partial
pivoting (GEPP) is numerically unstable. It has been known since
Wilkinson's work that, theoretically, GEPP can be unstable because of
the "growth factor," but many researchers have believed that this
instability does not occur in practical problems. Because of examples
like Foster's and other recent works, implementors of GEPP including
the LAPACK designers are planning to build additional safeguards into
software to detect unstable behavior.

In addition to these plenary talks, there were a total of 18
informal sessions spread over three evenings. One very popular
session was organized by Cleve Moler to demonstrate upcoming
developments in Matlab, which is an interactive software package for
numerical computation by The Mathworks, Inc. Moler demonstrated some
of the features of the latest version of Matlab and gave a preview of
a toolbox under development that integrates Maple, a symbolic
mathematics package from University of Waterloo, with Matlab.
Underscoring the informal nature of the meeting, one session (on
geometry, eigenvalues, and optimization, organized by Alan Edelman) was
held at the conference center's outdoor picnic area.

For the first time at a Householder meeting, laptop computers played
an important scientific role as many participants demonstrated
software to one another and conducted experiments during the breaks.
One use of the laptops, which were provided by UCLA and Cleve Moler,
was to analyze an impromptu graph made at the meeting showing
coauthorship relationships among participants. The graph was started
by Nick Trefethen, but most of the participants joined in. Gene Golub
turned out to have by far the greatest number of coauthors.

In addition to the technical presentations, there were many
recreational activities available at the scenic conference site. Boat
tours for the participants showed off the beauty of Lake Arrowhead and
the surrounding palatial summer homes owned by movie stars. Petter
Bjorstad led 16 people on a hike up Mount San Gorgonio, six of whom
went to the summit at 11,499 feet.

Two milestones were celebrated at the meeting. Gene Golub was feted
for his recent election to the National Academy of Sciences, and Alan
Edelman turned 30 at the meeting. Congratulations to Gene and Alan!
Charlie Van Loan collected funds from participants for a gift
certificate for Babette Dalton to thank her for her hard work on

The next Householder meeting is scheduled for 1996 in Switzerland. As
Martin Gutknecht said, the organizers of the Lake Arrowhead meeting,
including Tony Chan, Gene Golub and Babette Dalton, have set a high
standard for future organizers!


From: E. B. Saff <>
Date: Wed, 7 Jul 93 16:13:12 EDT
Subject: Contents: Constructive Approximation


Volume 9 Number 4 1993

Robert Schaback
Planar Curve Interpolation by Piecewise Conics of Arbitrary Type

Yongsheng Sun and Yongpins Liu
Optimal Recovery of the Sobolev-Wiener Class of Smooth Functions by
Double Sampling

R.K. Beatson and W.A. Light
Quasi-interpolation by Thin-Plate Splines on a Square

S.P. Zhou
On Muntz Rational Approximation

P. Binev, P. Petrushev, E.B. Saff, and O. Trifonov
Distribution of Interpolation Points of Best L_2-Approximants

Glenn M. Lilly and Stephen C. Milne
The C_l Bailey Transform and Bailey Lemma

Thomas Bagby, Aurel Cornea, and P.M. Gauthier
Harmonic Approximation on Arcs

J. Borwein, P. Borwein, and F. Garvan
Hypergeometric Analogues of the Arithmetic-Geometric Mean Iteration

Serge Dubuc and Fahima Nekka
General Interpolation Schemes for the Generation of Irregular Surfaces

D.J. Newman and Yuan Xu
Tchebycheff Polynomials on a Triangular Region


From: Iain Duff <>
Date: Mon, 5 Jul 93 10:23:04 GMT
Subject: Contents: IMA Journal of Numerical Analysis

IMA Journal of Numerical Analysis.
Volume 13 Number 3.
July 1993.

Raydan M
On the Barzilai and Borwein choice of steplength for the gradient method.

Coope I D
Curve interpolation with nonlinear spiral splines.

Tsao N K and Sun T C
On the numerical computation of the derivatives of a B-spline series.

Hu Y
An algorithm for data reduction using splines with free knots.

Williams J and Kalogiratou Z
Best Chebyshev approximation from families of ordinary differential equations.

Hosea M E and Shampine L F
Global extrapolation integrators for solving Sturm-Liouville problems by

Huang W and Sloan D M
A new pseudospectral method with upwind features.

Manoranjan V S and Drake R
A spectrum enveloping technique for convection-diffusion computations.

Elliott D
An asymptotic analysis of two algorithms for certain Hadamard finite-part

Rodriguez G and Seatzu S
On the numerical inversion of the Laplace transform in reproducing kernel
Hilbert spaces.

Koehler P
Error estimates for generalized compound quadrature formulas.


From: Laurenz Baltzer <>
Date: Tue, 6 Jul 1993 14:42:08 +0200
Subject: Contents: Advances in Computational Mathematics


John C. Mason
Applied & Computational Mathematics Group
Royal Military College of Science
Shrivenham, Swindon, SN6 8LA

Charles A. Micchelli
Mathematical Sciences Department
IBM Research Center
P.O. Box 218
Yorktown Heights, NY 10598
e-mail: cam@yktvmz.bitnet

Volume 1, no. 1

W. Dahmen & C.A. Micchelli, Continuous refinement equations and subdivision

P.J. van der Houwen, Preconditioning in implicit initial value problem
methods on parallel computers

H.N. Mhaskar, Approximation properties of a multilayered feedforward
artificial neural network

A.R. Champneys & A. Spence, Hunting for homoclinic orbits in reversible
systems: a shooting technique

T.N.T. Goodman, S.L. Lee & W.S. Tang, Wavelet bases for a set of commuting
unitary operators

R.E. Bank & C.C. Douglas, Sparse matrix multiplication package (SMMP)

Volume 1, no. 2

P.J. Barry, R.N. Goldman & C.A. Micchelli, Knot insertion algorithms for
piecewise polynomial spaces determined by connection matrices

J.M. Carnicer & J. M. Pena, Shape preserving representations and
optimality of the Bernstein basis

R.A. DeVore, G. Kyriazis, D. Leviaton & V.M. Tikhomirov,
Wavelet-compression and nonlinear n-widths

D.E. Gonsor, Nonnegative masks and stationary subdivision

W.B. Liu & J.W. Barrett, Error bounds for the finite element approximation
of a degenerate quasilinear parabolic variational inequality

L. Reichel, Construction of polynomials that are orthogonal with respect to
a discrete bilinear form

Orders and requests for sample copies to be sent to J.C. Baltzer AG,
Science Publishers, Wettsteinplatz 10, CH-4058 Basel, Switzerland, fax:
+41-61-692-42-62, e-mail:

Laurenz Baltzer
J.C.Baltzer AG, Science Publishers
Asterweg 1A
1031 HL Amsterdam
The Netherlands
Tel: +31 20 6370061
Fax: +31 20 6323651


From: Laurenz Baltzer <>
Date: Tue, 6 Jul 1993 14:47:26 +0200
Subject: Contents: Numerical Algorithms


Claude Brezinski
Laboratoire d'Analyse Numerique et d'Optimization
Universite des Sciences et Techniques de Lille
59655 Villeneuve d' Ascq Cedex
fax: +33-20-43-49-95
e-mail: brezinsk@frcitl81.bitnet

VOLUME 4, NO. 3:

Y. Xu, W.A. Light and E.W. Cheney, Constructive methods of approximation by
ridge functions and radial functions

P. Levrie and A. Bultheel, A note on Thiele n-fractions

M.A. Diniz-Ehrhardt and J.M. Martinez, A parallel projection method for
overdetermined nonlinear systems of equations

Nguyen huu Cong, A-stable diagonally implicit Runge-Kutta-Nystrom methods
for parallel computers

M. Calvo, J.I. Montijano and L. Randez, On the change of step size in
multistep codes

VOLUME 4, NO. 4:

S. Durand, Convergence of cascade algorithms introduced by I. Daubechies

K. Strom, Products of B-patches

C. Clavero and F. Lisbona, Uniformly convergent finite difference methods
for singularly perturbed problems with turning points

K. Jbilou, A general projection algorithm for solving systems of linear

P. Joly and G. Meurant, Complex conjugate gradient methods

Orders and requests for sample copies to be sent to J.C. Baltzer AG,
Science Publishers, Wettsteinplatz 10, CH-4058 Basel, Switzerland, fax:
+41-61-692-42-62, e-mail:

Laurenz Baltzer
J.C.Baltzer AG, Science Publishers
Asterweg 1A
1031 HL Amsterdam
The Netherlands
Tel: +31 20 6370061
Fax: +31 20 6323651


From: SIAM <>
Date: Tue, 06 Jul 93 11:40:15 EST
Subject: Contents: SIAM Numerical Analysis

Table of Contents
SIAM J. Numer. Anal., 30-5
October 1993

The Relative Efficiency of Alternative Defect Control Schemes
for High Order Continuous Runge--Kutta Formulas
W. H. Enright

Second-Order Accurate Difference Methods for a One-Sex Model
of Population Dynamics
Yong Hoon Kwon and Chung-Ki Cho

Continuous and Numerical Analysis of a Multiple Boundary
Turning Point Problem
Relja Vulanovic and Paul A. Farrell

New Error Bounds for the Quadrature Method for the Solution
of Cauchy Singular Integral Equations
Dietmar Berthold and Peter Junghanns

Sizing and Least Change Secant Methods
J. E. Dennis, Jr. and H. Wolkowicz

Need Title
Krishna and Wang

Domain Decomposition Type Iterative Techniques for Parabolic
Problems on Locally Refined Grids
R. E. Ewing, R. D. Lazarov, J. E. Pasciak, and P. S. Vassilevski

On the Identification Property of a Projected Gradient Method
P. L. De Angelis and G. Toraldo

Convergence Rates for Maximum Entropy Regularization
Heinz W. Engl and Gerhard Landl

A Stability Result for Sectorial Operators in Banach Spaces
C. Palencia

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

Ordering Effects of Relaxation Methods Applied to the Discrete One-
Dimensional Convection-Diffusion Equation
Howard C. Elman and Michael P. Chernesky

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

Godunov-Mixed Methods for Advection-Diffusion Equations in
Clint Dawson

Optimal a Posteriori Parameter Choice for Tikhonov Regularization
for Solving Nonlinear Ill-Posed Problems
O. Scherzer, H. W. Engl, and K. Kunisch

Differential Interpolants for High-Order Runge--Kutta Methods
J. H. Verner

On Entropy Consistency of Large Time-Step Schemes I. The Godunov
and Glimm Schemes
Gerald Warnecke and Jinghua Wang

On Entropy Consistency of Large Time-Step Schemes II. Approximate
Riemann Solvers
Gerald Warnecke and Jinghua Wang

Convergence Results for a Coordinate Projection Method Applied to
Mechanical Systems with Algebraic Constraints
Edda Eich

A Dissipative Pseudo-Spectral Method for the Two-Dimensional
Navier--Stokes Equations
K. Ito and S. Kang


End of NA Digest