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ARPACK Users' Guide

ARPACK Users' Guide
Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods


Part of Software, Environments and Tools

  • Date Published: April 1998
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898714074

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About the Authors
  • 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.

    Reviews & endorsements

    'This is a very useful book that follows the tradition of LINPACK and LAPACK users' guides. The book is well-written, precise, and does not lead to confusion. The required theory is also well-presented. We have used the package, following the guidelines in the users' guide successfully.' Henk van der Vorst

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    Product details

    • Date Published: April 1998
    • format: Paperback
    • isbn: 9780898714074
    • length: 158 pages
    • dimensions: 255 x 180 x 14 mm
    • weight: 0.348kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    List of figures
    List of tables
    1. Introduction to ARPACK. Important features
    Getting started
    Reverse communication interface
    Dependence on LAPACK and BLAS
    Expected performance
    Contributed additions
    Trouble shooting and problems
    2. Getting started with ARPACK. Directory structure and contents
    Getting started
    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 drivers
    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

  • Authors

    R. B. Lehoucq, Sandia National Laboratories, New Mexico

    D. C. Sorensen, Rice University, Houston

    C. Yang

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