ARPACK Users' Guide

Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods

AvR.B. Lehoucq,D.C. Sorenson

Häftad, Engelska, 1998

Del i serien Software Environments and Tools

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Beskrivning

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.

Produktinformation

Utgivningsdatum:1998-04-30
Mått:151 x 228 x 13 mm
Vikt:360 g
Format:Häftad
Språk:Engelska
Serie:Software Environments and Tools
Antal sidor:157
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9780898714074

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Recensioner i media

'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

Innehållsförteckning

List of FiguresList of TablesPrefaceChapter 1: Introduction to ARPACK. Important FeaturesGetting StartedReverse Communication InterfaceAvailabilityInstallationDocumentationDependence on LAPACK and BLASExpected PerformanceP_ARPACKContributed AdditionsTrouble Shooting and ProblemsChapter 2: Getting Started with ARPACK. Directory Structure and ContentsGetting StartedAn Example for a Symmetric Eigenvalue ProblemChapter 3: General Use of ARPACK. Naming Conventions, Precisions, and TypesShift and Invert Spectral Transformation ModeReverse Communication Structure for Shift-InvertUsing the Computational ModesComputational Modes for Real Symmetric ProblemsPostprocessing for Eigenvectors Using dseupdComputational Modes for Real Nonsymmetric ProblemsPostprocessing for Eigenvectors Using dneupdComputational Modes for Complex ProblemsPostprocessing for Eigenvectors Using zneupdChapter 4: The Implicitly Restarted Arnoldi Method. Structure of the Eigenvalue ProblemKrylov Subspaces and Projection MethodsThe Arnoldi FactorizationRestarting the Arnoldi MethodThe Generalized Eigenvalue ProblemStopping CriterionChapter 5: Computational Routines. ARPACK subroutinesLAPACK routines used by ARPACKBLAS routines used by ARPACKAppendix A: Templates and Driver Routines. Symmetric DriversReal Nonsymmetric DriversComplex DriversBand DriversThe Singular Value DecompositionAppendix B: Tracking the Progress of ARPACK. Obtaining Trace OutputCheck-Pointing ARPACKAppendix C: The XYaupd ARPACK RoutinesDSAUPDDNAUPDZNAUPDBibliographyIndex.