NA Digest Sunday, June 23, 1991 Volume 91 : Issue 25

Today's Editor: Cleve Moler

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From: David Rabson <>
Date: 18 Jun 91 17:21:41 GMT
Subject: Sparse Matix Eigenvals: Lanczos vs. Householder?

I need to diagonalize some very sparse matrices (density less than
5 per row of at least 1300) and wish very much to avoid fill-in.

I had thought that Lanczos would give only the highest and lowest
eigenvalues, but recently someone suggested that some modification
could tell me whether or not there was an eigenvalue or were
eigenvalues in any interval I chose to request. For my purposes,
I know that all eigenvalues lie between -5 and +5, and it would suffice
to split this range into a few thousand intervals and ask if there
were eigenvalue(s) in each such interval. What really interests me
is the pattern of intervals with NO eigenvalues.

On the other hand, Tewarson (Sparse Matrices, Ch. 7) discusses a pivoting
technique applicable to Givens or to Householder tridiagonalization that
apparently minimizes fill-in.

Does anyone have opinions on the relative merits and disadvantages
of these two approaches?

Are there public-domain routines available for anonymous FTP?

David Rabson
Departments of Physics, University of British Columbia
and McMaster University (Internet)


From: Richard Brualdi <>
Date: Mon, 17 Jun 91 06:54:16 cdt
Subject: Contents: Linear Algebra and Its Applications

Table of Contents, Volumes 154-56, Aug-Oct 1991

Iterations in Linear Algebra and Its Applications

Special Editors: O. Axelsson, J. de Pillis, M. Neumann,
W. Niethammer, and R. J.

A. Hadjidimos and A. K. Yeyios (West Lafayette, Indiana)
Some Recent Results on the Modified SOR Theory

Douglas James (Raleigh, North Carolina)
Order-Reducing Conjugate Gradients versus Block AOR
for Constrained Least-Squares Problems

Josep E. Peris (Alicante, Spain)
A New Characterization of Inverse-Positive Matrices

Shmuel Friedland (Chicago, Illinois)
Revisiting Matrix Squaring

Pierre Semal (Louvain-la-Neuve, Belgium)
Iterative Algorithms for Large Stochastic Matrices

Miron Tismenetsky (Heidelberg, Germany)
A Decomposition of Toeplitz Matrices and Optimal
Circulant Preconditioning

Ananda D. Gunawardena (Houston, Texas), S. K. Jain,
and Larry Snyder (Athens, Ohio)
Modified Iterative Methods for Consistent Linear Systems

Kimon Kontovasilis (Raleigh, North Carolina),
Robert J. Plemmons (Winston-Salem, North Carolina),
and William J. Stewart (Raleigh, North Carolina)
Block Cyclic SOR for Markov Chains with p-Cyclic Infinitesimal Generator

Biswa Nath Datta (DeKalb, Illinois) and Youcef Saad
(Minneapolis, Minnesota)
Arnoldi Methods for Large Sylvester-Like Observer Matrix
Equations, and an Associated Algorithm for Partial Spectrum Assignment

A. V. Knyazev and A. L. Skorokhodov (Moscow, USSR)

Roland Freund (Wu@a2rzburg, Germany)
On Polynomial Preconditioning and Asymptotic Convergence
Factors for Indefinite Hermitian Matrices

Ronald B. Morgan (Columbia, Missouri)
Computing Interior Eigenvalues of Large Matrices

L. Elsner (Bielefeld, Germany), M. Neumann
(Storrs, Connecticut), and B. Vemmer (Bielefeld, Germany)
The Effect of the Number of Processors on the Convergence of
the Parallel Block Jacobi Method

M. Tismenetsky (Haifa, Israel)
A New Preconditioning Technique for Solving Large Sparse Linear Systems

Gerhard Starke and Wilhelm Niethammer (Karlsruhe, Germany)
SOR for AX - XB=C

Dianne P. O'Leary (College Park, Maryland)
Yet Another Polynomial Preconditioner for the Conjugate Gradient

Lothar Reichel (Lexington, Kentucky)
The Application of Leja Points to Richardson Iteration and
Polynomial Preconditioning

William F. Trench (San Antonio, Texas)
Numerical Solution of the Eigenvalue Problem for Efficiently
Structured Hermitian Matrices

Yongzhong Song (Nanjing, Peoples' Republic of China)
omparisons of Nonnegative Splittings of Matrices

Martin Hanke (Karlsruhe, Germany), Michael Neumann
(Storrs, Connecticut), and Wilhelm Niethammer (Karlsruhe, Germany)
On the Spectrum of the SOR Operator for Symmetric Positive
Definite Matrices

Wang Deren (Shanghai, Peoples' Republic of China)
On the Convergence of the Parallel Multisplitting AOR Algorithm

Amit Bhaya, Eugenius Kaszkurewicz, and Francisco Mota
(Rio de Janeiro, Brazil)
Asynchronous Block-Iterative Methods for Almost Linear Equations

Tsun-Zee Mai (Tuscaloosa, Alabama)
Composite Adaptive Procedure for Solving Large Sparse Linear Systems

Z. Strakos (Praha, Czechoslovakia)
On the Real Convergence Rate of the Conjugate Gradient Method

J. de Pillis (Riverside, California)
A Parallelizable SOR-Like Method: Systems With Plus-Shaped
and Linear Spectra

Monga-Made Magolu and Yvan Notay (Bruxelles, Belgium)
On the Conditioning Analysis of Block Approximate
Factorization Methods

Alvaro R. De Pierro (Campinas, Brazil) and Alfredo N. Iusem
Rio de Janeiro, Brazil)
On the Convergence of SOR- and JOR-Type Methods for
Convex Linear Complementarity Problems

Paul E. Saylor (Zu@a2rich, Switzerland) and Dennis C. Smolarski
(Santa Clara, California)
Implementation of an Adaptive Algorithm for Richardson's Method

I. E. Kaporin (Moscow, USSR), L. Yu. Kolotilina
(Leningrad, USSR), and A. Yu. Yeremin (Moscow, USSR)
Block SSOR Preconditioning for High-Order 3D FE Systems.
II. Incomplete BSSOR Preconditionings

Sabine Van Huffel (Heverlee, Belgium)
Iterative Algorithms for Computing the Singular Subspace of a
Matrix Associated With Its Smallest Singular Values

Yvan Notay (Bruxelles, Belgium)
Conditioning Analysis of Modified Block Incomplete Factorizations

Victor Eijkhout (Urbana, Illinois)
Analysis of Parallel Incomplete Point Factorizations

Angelika Bunse-Gerstner and Ludwig Elsner (Bielefeld, Germany)
Schur Parameter Pencils for the Solution of the Unitary Eigenproblem

Ivo Marek (Praha, Czechoslovakia) and Daniel B. Szyld
(Philadelphia, Pennsylvania)
Pseudoirreducible and Pseudoprimitive Bounded Operators

Achiya Dax (Jerusalem, Israel)
A Row Relaxation Method for Large I1 Problems

Jerome Dancis (College Park, Maryland)
The Optimal w Is Not Best for the SOR Iteration Method

Special Issues in Progress

1. Algebraic Linear Algebra; special editors are Robert M. Guralnick, William
H. Gustafson, and Lawrence S. Levy. To appear as Volume 157, October 15, 1991.

2. Proceedings of the Auburn 1990 Matrix Theory Conference; special editors
are David Carlson and Frank Uhlig. Submission deadline: August 1, 1990.
Details provided with the conference announcement.

3. Proceedings of the Sixth Haifa Conference on Matrix Theory; special editors
are A. Berman, M. Goldberg, and D. Hershkowitz. Submission
deadline: October 1, 1990. Details provided with the conference announcement.

4. Proceedings of the International Workshop on Linear Models, Experimental
Designs and Related Matrix Theory, (August 6-8, 1990, Tampere, Finland);
special editors are Jerzy K. Baksalary and George Styan.
Submission deadline: October 31, 1990.
Details provided with the conference announcement.

5. Proceedings of the Second NIU Conference on Linear Algebra, Numerical
Linear Algebra and Applications, (May 3-5, 1991, Northern Illinois
University, DeKalb, Illinois); special editors are Biswa Datta, Robert
Plemmons, and Roger Horn. Submission deadline: August 31, 1991. Details
provided with the conference announcement.

Special issues are available to individuals at a reduced rate. For further
infor mation, please contact Bob Biederman, Journals Customer Service,
Elsevier Science Publishing Co., 655 Avenue of the Americas, New York, NY 10010;
Tel. 212- 633-3 955; Fax 212-633-3990.


Date: Thu, 20 Jun 91 15:44:03 IST
From: Danny Hershkowitz <MAR23AA%TECHNION@TAUNIVM.TAU.AC.IL>
Subject: 2nd ILAS Meeting


August 3-7, 1992
University of Lisbon


The Second Meeting of The International Linear Algebra Society
(ILAS) will be held at the University of Lisbon, Portugal, on
August 3-7, 1992.

There will be about twelve one-hour invited talks and twenty
eight half-hour invited talks. Also, we wish to encourage
contributed 15-20 minute talks, subject to the unavoidable
limitations of space and time. If you are interested in giving a
contributed talk at the conference, please send a title and an
abstract, to be received by us no later than May 1992. The title
and the abstract should be sent to Professor J.A. Dias Da Silva,
at the address given below.

A special issue of Linear Algebra and its Applications will be
devoted to the meeting. This issue will contain only papers that
meet the publication standards of the journal, and that are
approved by normal refereeing procedures. The issue will also
contain synopses of the talks of those invited speakers who do
not submit a paper to the proceedings. Special editors of this
issue are Professors J.A. Dias Da Silva, Chi-Kwong Li and G.N. de

Further information about the conference (when available) will be
sent upon request.

The organizing Committee of the meeting consists of:


Professor J.A. Dias Da Silva
Departamento de Matematica
da Universidade de Lisboa
Rua Ernesto de Vasconcelos, Bloco C1
1700 Lisboa
E-mail address: mperdiga@ptearn.BITNET


Professor David H. Carlson
Dept. of Mathematical Sciences
College of Sciences
San Diego State University
San Diego, CA 92182-0314
E-mail address: sdsu!

Professor Daniel Hershkowitz
Mathematics Department
Technion - Israel Institute of Technology
Haifa 32000

Professor Thomas J. Laffey
Mathematics Department
University College, Belfield,
Dublin, 4,

Professor G.N. de Oliveira
Departamento de Matematica
Universidade de Coimbra
3000 Coimbra

Professor Hans Schneider
Mathematics Department
Van Vleck Hall
University of Wisconsin - Madison
WI 53706
E-mail address:


End of NA Digest