The refined harmonic Arnoldi method and an implicitly restarted refined algorithm for computing interior eigenpairs of large matrices
type: Item
instance of: scholarly article
title: The refined harmonic Arnoldi method and an implicitly restarted refined algorithm for computing interior eigenpairs of large matrices
zbMATH Open document ID: 1030.65023
DOI: 10.1016/S0168-9274(01)00132-5
author: Zhongxiao Jia
published in: Applied Numerical Mathematics
publication date: 2003-03-10T00:00:00Z
review text: The author proposes a new variant of the implicitly restarted Arnoldi algorithm, called the implicitly restarted refined harmonic Arnoldi algorithm (IRRHA-adding one more acronym to the long list of Krylov subspace methods). It is suited to find interior eigenvalues when a shift and invert strategy is deemed as unfeasible. The use of refined shifts (which are better approximations to eigenvalues than the not-refined ones) is responsible for the superior performance. This is motivated by an interesting theorem, which suggest that in exact arithmetic the exact eigenvalues can be found with a small number of restarts. The paper concludes with numerical examples and tests which show the superior performance of the new algorithm.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1879059
zbMATH Keywords: implicitly restarted Arnoldi algorithm
zbMATH Keywords: refined harmonic Arnoldi method
zbMATH Keywords: interior eigenvalue
zbMATH Keywords: refined shifts
zbMATH Keywords: Krylov subspace methods
zbMATH Keywords: shift and invert strategy
zbMATH Keywords: numerical examples
Wikidata QID: Q56457285
reviewed by: Hermann G. Matthies
describes a project that uses: eigs
describes a project that uses: JDQR
describes a project that uses: JDQZ
describes a project that uses: ARPACK
describes a project that uses: Harwell-Boeing sparse matrix collection
describes a project that uses: IRAM
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1879059