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: Book/ReportReportAcademic

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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. Key words: Field of values, numerical range, matrix inverse, large sparse matrix, Ritz values, harmonic Rayleigh-Ritz, harmonic Ritz values, GMRES convergence, Arnoldi, numerical radius, numerical abscissa, inner numerical radius, inclusion region.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages11
Publication statusPublished - 2013

Publication series

NameCASA-report
Volume1308
ISSN (Print)0926-4507

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