Numerical approximation of the field of values of the inverse of a large matrix

M.E. Hochstenbach, D.A. Singer, P.F. Zachlin

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Abstract

We consider the approximation of the field of values of the inverse of a large sparse matrix, without explicitly computing the inverse or using its action (i.e., accurately solving a linear system with this matrix). We review results by Manteuffel and Starke and give an alternative that may yield better approximations in practice. We give connections with the harmonic Rayleigh-Ritz approach. Several properties and applications of the studied concepts as well as numerical examples are provided.
Original languageEnglish
Title of host publicationThe Natália Bebiano anniversary volume
EditorsC. Fonseca, S. Furtado, A. Kovacec, C.-K. Li
Place of PublicationCoimbra
PublisherUniversity of Coimbra
Pages59-71
ISBN (Print)978-972-8564-48-3
Publication statusPublished - 2013

Publication series

NameTextos de Matemática
Volume44

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