ARPACK users' guide : solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods / R.B. Lehoucq, D.C. Sorensen, C. Yang.

Format:

Book

Author/Creator:

Lehoucq, R. B. (Richard B.)

Contributor:

Sorensen, D. C. (Danny C.)

Yang, C. (Chao)

Society for Industrial and Applied Mathematics.

Series:

Software, environments, tools ; 6.

Software, environments, tools ; 6

Language:

English

Subjects (All):

ARPACK (Computer file).

Eigenvalues--Data processing.

Eigenvalues.

Physical Description:

1 electronic text (xv, 142 p.) : ill., digital file.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1998.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

This book is a guide to understanding and using the software package ARPACK to solve large algebraic eigenvalue problems. The software described is based on the implicitly restarted Arnoldi method, which has been heralded as one of the three most important advances in large scale eigenanalysis in the past ten years. The book explains the acquisition, installation, capabilities, and detailed use of the software for computing a desired subset of the eigenvalues and eigenvectors of large (sparse) standard or generalized eigenproblems. It also discusses the underlying theory and algorithmic background at a level that is accessible to the general practitioner.

Contents:

List of figures

List of tables

Preface

1. Introduction to ARPACK

Important features

Getting started

Reverse communication interface

Availability

Installation

Documentation

Dependence on LAPACK and BLAS

Expected performance

P_ARPACK

Contributed additions

Trouble shooting and problems

2. Getting started with ARPACK

Directory structure and contents

An example for a symmetric eigenvalue problem

3. General use of ARPACK

Naming conventions, precisions, and types

Shift and invert spectral transformation mode

Reverse communication structure for shift-invert

Using the computational modes

Computational modes for real symmetric problems

Postprocessing for eigenvectors using dseupd

Computational modes for real nonsymmetric problems

Postprocessing for eigenvectors using dneupd

Computational modes for complex problems

Postprocessing for eigenvectors using zneupd

4. The implicitly restarted Arnoldi method

Structure of the eigenvalue problem

Krylov subspaces and projection methods

The Arnoldi factorization

Restarting the Arnoldi method

The generalized eigenvalue problem

Stopping criterion

5. Computational routines

ARPACK subroutines

LAPACK routines used by ARPACK

BLAS routines used by ARPACK

Appendix A. Templates and driver routines

Symmetric Drivers

Real nonsymmetric drivers

Complex divers

Band drivers

The singular value decomposition

Appendix B. Tracking the progress of ARPACK

Obtaining trace output

Check-pointing ARPACK

Appendix C. The XYaupd ARPACK routines

DSAUPD

DNAUPD

ZNAUPD

Bibliography

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 133-136) and index.

Title from title screen, viewed 12/30/2010.

ISBN:

0-89871-962-3

Publisher Number:

SE06 SIAM