- Today's Editor:
- Cleve Moler
- The MathWorks, Inc.
- moler@mathworks.com

- 100-dollar, 100-digit Challenge
- Singular Value Distribution of Noise Corrupted Data Matrices
- A Matrix Optimization Problem
- New Book, Handbook of Numerical Analysis
- New Book Series, Numerical Methods and Algorithms
- Bay Area Scientific Computing Day 2002
- SIAM Conference on Applied Linear Algebra
- Minisimposium in Bulgaria on Control and Uncertain Systems
- Chemnitz FEM Symposium
- Software Demonstrations at ISSAC
- Symposium in Romania on Parallel and Distributed Computing
- Beijing Satellite Conference on Scientific Computing
- Faculty Position at UNC Charlotte
- Faculty Position at the University of the Witwatersrand
- Research Positions at National University of Singapore
- Research Position at University of Erlangen
- Contents, Electronic Transactions on Numerical Analysis
- Subscribe, unsubscripe, change address, or for na-digest archives:
- http://www.netlib.org/na-net

Information via e-mail about NA-NET:
* Mail to na.help@na-net.ornl.gov.*

-------------------------------------------------------

From: Nick Trefethen <lnt@comlab.ox.ac.uk>

Date: Thu, 31 Jan 2002 10:16:17 GMT

**Subject: 100-dollar, 100-digit Challenge**

I would like to draw NA-Digest subscribers' attention to the

"Hundred-dollar, hundred-digit challenge" just published in

the Jan/Feb 2002 issue of SIAM News, and available online at

http://www.siam.org/siamnews/01-02/challenge.pdf. The

challenge consists of ten computational problems, each of

whose answers is a single real number. The person or

group who manages to calculate the greatest number of correct

digits by May 20, 2002, up to ten digits for each of the ten

problems, will win $100 and be mentioned in SIAM News.

The challenge can serve nicely as the focus of a student

problem-solving club. I am curious to see how many digits we get!

Nick Trefethen, Oxford University

------------------------------

From: Nils Wagner <nwagner@mecha.uni-stuttgart.de>

Date: Wed, 30 Jan 2002 10:40:32 +0100

**Subject: Singular Value Distribution of Noise Corrupted Data Matrices**

Dear NA Readers,

Given a real matrix Z with n rows and m columns (m >> n) and a random

matrix R (with uniformly distributed random numbers in the range \pm 1),

I would like to find a prediction of the singular value distribution of

Z in comparison to Z+G*R, where G = z_max*(p/100)*I is a diagonal matrix.

I denotes the identity matrix. p is the noise level and z_max denotes

the maximum absolute value of all elements of Z.

Does anyone know of any references for this problem ?

Thanks in advance.

Nils Wagner

------------------------------

From: Hao Lu <hao.lu_2@philips.com>

Date: Thu, 31 Jan 2002 09:17:45 +0100

**Subject: A Matrix Optimization Problem**

Motion estimation is the core part of video (moving image) compression

and has attracted much attention because of the following reasons:

a. It consumes 60-80% of computing time of a video encoder, which limits

the encoding speed.

b. A motion estimation algorithm has a high impact on the visual

performance of an encoder for a given bit rate.

The major application of the problem is in multimedia communication,

TV broadcasting, video conference, video recorders, mobile communication

and so on.

The motion estimation problem is equivalent to a matrix optimization

problem. Let me describe the problem in terms of matrices. Let A=(a_ij)

be an nxm matrix. Define an adjacent pxq submatrix A_ij by a pxq submatrix

of A of the form

/ a_ij a_i, j+1 ... a_i, j+q-1 \

| a_i+1, j a_i+1, j+1 ... a_i+1, j+q-1 |

A_ij = | ............................................. |

\ a_i+p-1, j a_i+p-1, j+1 ... a_i+p-1, j+q-1 /

Let B=(b_ij) be a pxq matrix. The problem is to design a fast algorithm

in finding an adjacent pxq submatrix A_ij of A such that the distance

||B-A_ij|| (or a norm) is minimized over the set of all pxq adjacent

submatrices of A. The trivial approach is the exhaust comparison that

computes distance of every pxq adjacent submatrix to B and finds the

solution by comparison, which is called the exhaust search in motion

estimation terminology. This approach needs O(pq(n-p)(m-q)) operations,

which is too expensive.

I post the problem as a matrix optimization problem here and share it

with some na-net readers who may be interested. If any one has a good

solution please send me e-mail.

Hao Lu

------------------------------

From: Andy Deelen <A.Deelen@elsevier.nl>

Date: Mon, 28 Jan 2002 20:17:09 +0100

**Subject: New Book, Handbook of Numerical Analysis**

Just published:

Handbook of Numerical Analysis, Volume VIII, edited by P.G. Ciarlet and J.L.

Lions, 2002, EUR 125 / US$ 125 / HARDBOUND / ISBN: 0-444-50906-2

Contents:

General Preface.

Solution of equations in Rn (Part 4): computational methods for large

eigenvalue problems (H.A. van der Vorst). Techniques of scientific computing

(Part 4): theoretical and numerical analysis of differential-algebraic

equations (P.J. Rabier, W.C. Rheinboldt). Numerical methods for fluids (Part

2): mathematical modeling and analysis of viscoelastic fluids of the oldroyd

kind (E. Fernandez-Cara, F. Guillen, R.R. Ortega).

More information can be found at the URL below:

http://www.elsevier.com/locate/inca/501439

SPECIAL OFFER

Elsevier is pleased to offer a 30% discount on the previous volumes of the

Handbook of Numerical Analysis (Volumes III, IV, V, VI and VII).

Please contact Andy Deelen at Elsevier (a.deelen@elsevier.nl) for a special

order form for these volumes.

More information on the previous volumes can also be found at:

http://www.elsevier.com/locate/inca/501439

Andy Deelen

Elsevier Science

Mathematics & Computer Science Department

P.O. Box 103

1000 AC Amsterdam

The Netherlands

------------------------------

From: Claude Brezinski <claude.brezinski@univ-lille1.fr>

Date: Tue, 29 Jan 2002 09:20:27 +0100

**Subject: New Book Series, Numerical Methods and Algorithms**

Kluwer Academic Publishers announce the

"Numerical Methods and Algorithms Book Series"

The series publishes monographs devoted to numerical methods

and algorithms, carefully selected proceedings, and reference

books such as handbooks.

Books can either have a theoretical nature or present algorithms,

software, and/or applications.

All areas of numerical analysis are taken into consideration:

general principles, numerical linear algebra, ordinary differential

equations, partial differential equations, integral equations,

difference equations, systems of nonlinear equations, interpolation

and approximation, splines, optimization, numerical quadrature and

cubature, linear and integer programming, computer arithmetic,

control theory, fractals, wavelets, etc. Books on computer

algebra concerned with obtaining numerical results are also welcome.

All aspects of algorithms are covered: new algorithms, theoretical

results, implementation on various computer architectures, numerical

stability, complexity, computational features, software, and

numerical questions which arise in different fields of applied science.

The audience for the books is advanced students (doctoral and

post-doctoral level), researchers and engineers in numerical analysis,

computer science, applied mathematics and in the various branches of

science concerned with numerical computations.

Proposals for the series should be sent by e-mail to its editor

Claude Brezinski at Claude.Brezinski@univ-lille1.fr

The first volume of the series will appear this spring:

C. Brezinski

"Computational Aspects of Linear Control"

Contents: control of linear systems, formal orthogonal polynomials,

Pade approximations, transform inversion, linear algebra issues,

Lanczos tridiagonalization process, systems of linear algebraic

equations, regularization of ill-conditioned systems, Sylvester and

Riccati equations, topics on nonlinear differential equations, the

mathematics of model reduction.

More information should be available on Kluwer's web site in a couple

of months time.

------------------------------

From: Tammy Kolda <tgkolda@sandia.gov>

Date: Mon, 28 Jan 2002 08:41:09 -0800

**Subject: Bay Area Scientific Computing Day 2002**

BAY AREA SCIENTIFIC COMPUTING DAY 2002

Saturday, March 2, 2002

Crowne Plaza Hotel, Pleasanton, CA

The Bay Area Scientific Computing Day is an informal gathering to

encourage the interaction and collaboration of researchers from the

San Francisco Bay Area in the field of scientific computing. It also

provides new researchers an opportunity to present their work to the

local community. This year's meeting will be held at the Crowne Plaza

Hotel at the intersection of 580 and 680 in Pleasanton. All are

invited to attend.

This one-day workshop will have nine 25-minute technical presentations

and a 60-minute poster session. A continental breakfast, lunch and two

refreshment breaks will be provided.

Web site: http://csmr.ca.sandia.gov/workshops/bascd2002/

Contributed Poster Submission Deadline: February 2, 2002

Registration Deadline: February 23, 2002

There is no registration fee. For further information, contact:

Vicki Howle, vehowle@sandia.gov, 925-294-2204

Jonathan Hu, jhu@sandia.gov, 925-294-2931

Tamara Kolda, tgkolda@sandia.gov, 925-294-4769

Monica Martinez-Canales, mmarti7@sandia.gov, 925-294-3157

Juan Meza, meza@sandia.gov, 925-294-2425

BASCD 2002 is sponsored by the Computer Science Research Institute at

Sandia National Labs.

------------------------------

From: Darrell Ross <ross@siam.org>

Date: Tue, 29 Jan 2002 16:01:35 -0500

**Subject: SIAM Conference on Applied Linear Algebra**

PRELIMINARY CONFERENCE ANNOUNCEMENT

July 15-19, 2003

SIAM Conference on Applied Linear Algebra (LA03)

The College of William and Mary, Williamsburg, VA

Sponsored by SIAM Activity Group on Linear Algebra (SIAG/LA)

In coorporation with the International Linear Algebra Society (ILAS)

Program Committee

CHAIRS:

Roy Mathias, The College of William and Mary

Hugo Woerdeman, The College of William and Mary

OTHER MEMBERS:

Raymond Chan, University of Hong Kong

John Gilbert, Xerox Co.

Per Christian Hansen, Technical University of Denmark

Nicholas Higham, University of Manchester

Ilse Ipsen, North Carolina State University

Horst Simon, National Energy Research Scientific Computing Center

Paul Van Dooren, Universite Catholique de Louvain

For upcoming details and updates, follow the website at:

http://www.siam.org/meetings/la03/

------------------------------

From: Svetoslav Markov <smarkov@iph.bio.bas.bg>

Date: Wed, 30 Jan 2002 18:54:55 +0100

**Subject: Minisimposium in Bulgaria on Control and Uncertain Systems**

Dear Colleagues,

We kindly invite you to attend the Minisymposium on

CONTROL AND UNCERTAIN SYSTEMS

organized by the Institute of Mathematics and Informatics (dept. of

Biomathematics and dept. of Operational Research) at

the Bulgarian Academy of Sciences, in the frames of the

Fifth International Conference on

Numerical Methods and Applications - NMA'02

August 20 - 24, 2002, Borovets, BULGARIA

More information about NMA'02 can be found on URL:

http://www.bas.bg/clpp/nma02.html

The aim of the Minisymposium CONTROL AND UNCERTAIN SYSTEMS

is to bring together mathematicians, specialists in control theory

and computer sciences, as well as specialists in applications

in natural and social sciences, and engineering. The program encourages

wide range of discussions by all participants on basic problems and

future directions. The accepted papers will be published in a

prestigious international book series.

The range of topics to be discussed in the minisymposium

includes amongst others:

- Numerical methods for control problems

(optimal control, stability, controllability, viability, sensitivity, etc.);

- Numerically oriented approaches for problems with uncertainties

(differential inclusions, problems with incomplete/inexact information,

differential games);

- Theory, algorithms and arithmetics for validated numerics;

- Applications in biology, biotechnology, ecology, medicine, economics,

engineering, social sciences etc.

- Hardware and software support for numerical methods in the above areas;

The deadline for submission of abstracts and registration forms for

the minisymposium is 30.03.2002. If you would like to present a paper for

publication in the proceedings, please submit it by the same date.

Detailed information about the registration and the submission of

abstracts and papers, as well as for the registration and accommodation

costs, can be found at the above WEB address.

V. Veliov <vveliov@e119ws1.tuwien.ac.at>

M. Krastanov <krast@math.bas.bg>

S. Markov <smarkov@bio.bas.bg>

------------------------------

From: Gerd Kunert <gerd.kunert@mathematik.tu-chemnitz.de>

Date: Wed, 30 Jan 2002 15:41:40 +0100

**Subject: Chemnitz FEM Symposium**

Dear colleagues,

We would like to invite you and your colleagues to the

Chemnitz FEM Symposium 2002

September 23 - 25, 2002.

The symposium takes place in Ehrenfriedersdorf near Chemnitz, Germany.

It is organized by the DFG-Sonderforschungsbereich 393

"Numerische Simulation auf massiv parallelen Rechnern"

and the Faculty of Mathematics, TU Chemnitz.

Scientific Topics: Finite Elements, including (but not limited to)

- fast solvers,

- error estimators,

- high order methods,

- parallel implementations.

This year special emphasis is on

- solution of elastic contact problems,

- anisotropic mesh generation and error estimation,

- PDEs in finance,

- wavelets discretizations.

Invited Speakers: H. Blum (Dortmund

W. Dahmen (Aachen)

J. Schoeberl (Linz)

L. Formaggia (Lausanne)

Important date: August 9, 2002: Submission of abstracts

Registration: via WWW

Information: http://www.tu-chemnitz.de/sfb393/fem-symposium/

Contact: fem02@mathematik.tu-chemnitz.de

The symposium is supported by the Deutsche Forschungsgemeinschaft.

With best regards

Th. Apel, A. Meyer, G. Kunert

------------------------------

From: ISSAC <Conference.Issac2002@lifl.fr>

Date: Fri, 1 Feb 2002 19:13:03 +0100 (MET)

**Subject: Software Demonstrations at ISSAC**

CALL FOR LIVE SOFTWARE DEMONSTRATIONS

ISSAC 2002

International Symposium on Symbolic and Algebraic Computation

University of Lille I, France, July 7-10, 2002

http://www.lifl.fr/issac2002

ISSAC is the yearly premier international symposium on Symbolic and

Algebraic Computation. It provides an opportunity to learn of new

developments and to present original research results in all areas of

symbolic mathematical computation.

This year ISSAC organises a new live software demonstration session.

Important Dates

30 April 2002: Software demonstration submissions must be received.

31 May 2002: Notification of acceptance.

This session is intended to promote software development activities in

the areas of symbolic mathematical computation.

To encourage submissions of good quality, two best demonstration

prizes will be awarded. Demonstrations will be judged by the program

committee and the attendees independently, booth based on content and

presentation.

Details are available at:

http://lifl.lifl.fr/issac2002/calldemos.html

------------------------------

From: Marcin Paprzycki <marcin@a.cs.okstate.edu>

Date: Fri, 1 Feb 2002 21:49:45 -0600 (CST)

**Subject: Symposium in Romania on Parallel and Distributed Computing**

CALL FOR PAPERS

International Symposium on Parallel and Distributed Computing

Iasi, Romania, 17-20 July, 2002

http://www.infoiasi.ro/~ispdc/dates.html

Sponsored by the IEEE Task Force on Cluster Computing

Held in conjuction with the European Conference on Intelligent Systems and

Technologies - ECIT and Romanian Symposium on Computer Science - ROSYCS

Prospective authors are invited to submit original unpublished papers

describing theoretical and/or experimental research, as well as position

papers. Specific areas of interest include, but are not limited to:

* models and formal verification

* programming paradigms and tools

* resource discovery and management

* task and communication scheduling

* performance management

* heterogeneous cluster computing

* grid computing

* mobile agent systems

* peer-to-peer computing

* adaptive computing

* ubiquitous computing

* mobile computing

* web distributed computing

* real-time distributed systems

* security

* fault tolerance

* application case studies

Papers should not exceed ten (10) single-spaced pages of text using

12-point size type on 8.5 x 11 inch pages. References, figures, tables,

etc., may be included in addition to the ten pages of text. The summary

should include an abstract of approximately 100 words. The corresponding

author is requested to include in a cover letter: (1) complete postal

address; (2) email address; and (3) phone/fax numbers.

Electronic submissions are preferred (pdf, ps, doc) and should be sent to

submit-ISPDC@infoiasi.ro. All submissions will be reviewed by referees.

The proceedings of this symposium will be published.

Important Dates

Paper submission deadline: February 28, 2002

Notification of acceptance: March 31, 2002

Camera-ready copies due: April 30, 2002

For more information, please see the conference WWW site at:

http://www.infoiasi.ro/~ispdc/dates.html

------------------------------

From: Zhangxin Chen <zchen@post.cis.smu.edu>

Date: Sat, 2 Feb 2002 11:04:29 -0600 (CST)

**Subject: Beijing Satellite Conference on Scientific Computing**

2ND Announcement and Call for Papers and Organizing Minisymposia

ICM2002-Beijing Satellite Conference on

Scientific Computing

Aug. 15--18, 2002

Xi'an Jiaotong University, Xi'an, China

http://www2.smu.edu/math/CSC/shouye.htm

http://www.xjtu.edu.cn/xjnet/temp/icm2002/shouye.htm

------------------------------

From: Wei Cai <wcai@uncc.edu>

Date: Sat, 2 Feb 2002 11:59:10 -0500 (EST)

**Subject: Faculty Position at UNC Charlotte**

University of North Carolina at Charlotte

Department of Mathematics

The Department of Mathematics invites applications for a tenure track

position at the Assistant Professor level in Computational Mathematics

beginning in August 2002.

Candidates must have a Ph.D. degree and demonstrated strength at research in

numerical analysis and a commitment to teaching. Preference will be given to

applicants with strong interdisciplinary research experience in developing

efficient algorithms to address computational problems arising in sciences

and engineering applications with potentials for external funding.

Send CV, three letters of recommendation, Statement of research and

teaching interests to Faculty Search Committee, Department of Mathematics,

University of North Carolina at Charlotte, Charlotte, NC 28223. Review of

applications will begin on February 18, 2002.

AA/EOE Women and underrepresented minorities are urged to apply.

http://www.math.uncc.edu/employment

------------------------------

From: Montaz Ali <mali@cam.wits.ac.za>

Date: Tue, 29 Jan 2002 22:21:56 +0200 (SAST)

**Subject: Faculty Position at the University of the Witwatersrand**

SCHOOL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Associate Professorship/Senior Lecturer/Lecturer

Applications are invited for the above positions from suitably qualified

candidates. Areas of interest in the School include numerical analysis,

optimization and control, image processing, differential equations,

continuum mechanics, astronomy, bio-mathematics, mathematics of finance,

mathematics in industry and mathematical modelling.

QUALIFICATIONS: PhD at least; research profile for senior posts;

leadership ability for professorships.

SALARY: This is negotiable. Additional benefits include contributions to

the provident fund, an annual bonus, generous leave, medical aid, housing

subsidy (if eligible), relocation allowance, 100% financial assistance of

dependent's university studies (if eligible).

ENQUIRIES: Prof D Sherwell, tel: (+27)(11) 717-6120, fax: (+27)(11)

403-9317, e-mail: sherwell@cam.wits.ac.za

An information sheet is available from the Human Resources Manager

(address below) or from our website: http://www.cam.wits.ac.za/

TO APPLY: Submit a detailed CV with the names, addresses and contact

details (e-mail addresses) of three referees and certified copies of

degrees/diplomas to: Prof D Sherwell, School of Computational and Applied

Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050,

Johannesburg, South Africa.

CLOSING DATE 15 FEBRUARY 2002

THE UNIVERSITY OF THE WITWATERSRAND IS COMMITTED TO EXCELLENCE AND EQUITY

------------------------------

From: Wong Wai Yeng <ieswwy@nus.edu.sg>

Date: Fri, 1 Feb 2002 10:01:27 +0800

**Subject: Research Positions at National University of Singapore**

Research Scientists and Associate Scientists

National University of Singapore

The Centre for Wavelets, Approximation and Information Processing (CWAIP)

(http://www.cwaip.nus.edu.sg/)

through Temasek Laboratories(http://www.temasek-lab.nus.edu.sg/) of the

National University of Singapore

(http://www.nus.edu.sg/) invites applications for the positions of Research

Scientists and Associate Scientists in the following areas:

Underwater signal processing;

Image, video and data compression;

Signal detection and identification;

Speech processing.

Successful candidates will be staff members of Temasek Laboratories working

on the research programme "Wavelets and Information Processing" in the CWAIP.

Further information about the research activities of the CWAIP and Temasek

Laboratories can be found in the following websites:

http://www.cwaip.nus.edu.sg/

http://www.temasek-lab.nus.edu.sg/

Responsibilities

Successful candidates are required to make significant contributions to the

research programme. This includes invention of new techniques and algorithms

in the related research areas and development of computer software systems.

Requirements

PhD/Master/Bachelor (Hons) degree holders in Engineering, Computer Science,

Mathematics, Physics or other related areas; Strong background and experience

in at least one of the areas of the programme; Knowledge and experience in

wavelets or underwater acoustics preferred.

Applications

Further enquiries and applications should be directed to:

Dr Goh Say Song (matgohss@nus.edu.sg)

Deputy Director

Centre for Wavelets, Approximation and Information Processing

Department of Mathematics

National University of Singapore

2 Science Drive 2

Singapore 117543

Only short-listed candidates will be notified. Application forms can be

downloaded from http://www.temasek-lab.nus.edu.sg/

------------------------------

From: Ulrich Ruede <Ulrich.Ruede@informatik.uni-erlangen.de>

Date: Fri, 1 Feb 2002 15:36:37 +0100 (CET)

**Subject: Research Position at University of Erlangen**

The "Lehrstuhl fuer Systemsimulation" at the University of Erlangen-Nuremberg

has an opening for a research assistant or post doc starting April 1, 2002.

This is a joint project between the Crystal Growth Laboratory and the

Institute of Computer Science at University of Erlangen. Project goal is

to develop and implement simulation programs for modeling and designing

high temperature furnaces in industry.

The research assistant at the "Lehrstuhl fuer Systemsimulation" will

be primarily responsible for developing and implementing discretization

techniques and fast solvers based on modern iterative techniques,

like Algebraic Multigrid and Conjugate Gradient methods. This will

require close collaboration with the Crystal Growth Laboratory, where the

physical models will be developed. Another project partner is University

of Erlangen's Lehrstuhl for Computer Graphics which will be responsible for

providing the software modules for geometry handling and visualization.

The ideal candidate will have a strong background in numerical

mathematics, iterative solvers, the numerics of PDE and Finite Element

Methods. However, the project also requires several years of experience

with modern programming languages (like C++) and software engineering

techniques.

The position requires a degree equivalent to the German Diploma (Master

of Science) and could then be combined with PhD thesis research. The

position would also be suitable for a post doc. The salary will be

according to the German BAT IIa. Since an intensive collaboration with

our project partners is essential, candidates with a knowlegde of German

will be given preference.

Applications and inquiries should be sent to

Ulrich Ruede

Lehrstuhl fuer Simulation

Universitaet Erlangen-Nuernberg

Cauerstr. 6

D-91058 Erlangen

Germany

e-mail: ruede@informatik.uni-erlangen.de

URL: http://www10.informatik.uni-erlangen.de/~ruede

------------------------------

From: Lothar Reichel <reichel@reichel.math.kent.edu>

Date: Mon, 28 Jan 2002 19:10:15 -0500 (EST)

**Subject: Contents, Electronic Transactions on Numerical Analysis**

Table of Contents, Electronic Transactions on Numerical Analysis (ETNA),

vol. 12, 2001. ETNA is available at http://etna.mcs.kent.edu and at several

mirror sites, as well as on CDROM.

G. Meurant, Numerical experiments with algebraic multilevel

preconditioners, pp. 1-65.

H. Zhang, Numerical condition of polynomials in different forms, pp. 66-87.

M. J. Castel, V. Migallo'n, and J. Penade's, On parallel two-stage methods

for Hermitian positive definite matrices with applications to preconditioning,

pp. 88-112.

R. S. Varga, Gersgorin-type eigenvalue inclusion theorems and their sharpness,

pp. 113-133.

F. B. Belgacem and S. C. Brenner, Some nonstandard finite element estimates

with applications to 3D Poisson and Signorini Problems, pp. 134-148.

S. Ehrich and A. Rathfeld, Piecewise linear wavelet collocation, approximation

of the boundary manifold, and quadrature, pp. 149-192.

J.-B. Chen and M.-Z. Qin, Multi-symplectic Fourier pseudospectral method for

the nonlinear Schrodinger equation, pp. 193-204.

B. Fischer and F. Peherstorfer, Chebyshev approximation via polynomial

mappings and the convergence behaviour of Krylov subspace methods, pp. 205-215.

A. A. Dubrulle, Retooling the method of block conjugate gradients, pp. 216-233.

E. J. McDonald and D. J. Higham, Error analysis of QR algorithms for computing

Lyapunov exponents, pp. 234-251.

------------------------------

End of NA Digest

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