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

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by R. B. Lehoucq, D. C. Sorensen, and C. Yang


1998 / xvi + 160 pages / Softcover / ISBN: 978-0-898714-07-4 / List Price $74.50 / SIAM Member Price $52.15 / Order Code SE06

"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

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.

Other important topics covered include

  • Treatment of the non-Hermitian problem,
  • Explanation of the theory behind Krylov subspace projection methods, implicit restarting, and spectral transformation,
  • Explanation of the implicitly restarted Arnoldi method (IRAM),
  • Descriptions of the various templates (driver routines) to interface an application with ARPACK to solve a wide variety of problems.

ARPACK is a collection of Fortran 77 subroutines designed to solve large-scale eigenvalue problems. It provides state-of-the-art software for solving large (sparse) Hermitian, non-Hermitian, standard, or generalized eigenvalue problems from significant application areas. It is one of the few software packages to successfully address the non-Hermitian problem. Practitioners will be able to better understand the full capabilities of ARPACK (ARnoldi PACKage) and grasp the underlying theory more thoroughly with this book.

This guide is intended for scientists and engineers who need to compute a selected subset of the eigenvalues and eigenvectors for a large sparse eigenproblem that is relevant to a specific application, and for researchers and developers of algorithms and software for numerical linear algebra.

List of Figures; List of Tables; Preface; Chapter 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; Chapter 2: Getting Started with ARPACK. Directory Structure and Contents; Getting Started; An Example for a Symmetric Eigenvalue Problem; Chapter 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; Chapter 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; Chapter 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; DNAUPD; ZNAUPD; Bibliography; Index.

ISBN: 9780898714074

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