Computing approximate (block) rational Krylov subspaces without explicit inversion with extensions to symmetric matrices

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dc.contributor.authorMach, Thomas
dc.contributor.authorPranić, Miroslav S.
dc.contributor.authorVandebril, Raf
dc.date.accessioned2017-01-09T11:00:15Z
dc.date.available2017-01-09T11:00:15Z
dc.date.issued2014
dc.description.abstractIt has been shown that approximate extended Krylov subspaces can be computed, under certain assumptions, without any explicit inversion or system solves. Instead, the vectors spanning the extended Krylov space are retrieved in an implicit way, via unitary similarity transformations, from an enlarged Krylov subspace. In this paper this approach is generalized to rational Krylov subspaces, which aside from poles at infinity and zero, also contain finite non-zero poles. Furthermore, the algorithms are generalized to deal with block rational Krylov subspaces and techniques to exploit the symmetry when working with Hermitian matrices are also presented. For each variant of the algorithm numerical experiments illustrate the power of the new approach. The experiments involve matrix functions, Ritz-value computations, and the solutions of matrix equations.ru_RU
dc.identifier.citationMach, T., Pranić, M. S., & Vandebril, R. (2014). Computing approximate (block) rational Krylov subspaces without explicit inversion with extensions to symmetric matrices. Electronic Transactions on Numerical Analysis, 43, 100-124.ru_RU
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/2228
dc.language.isoenru_RU
dc.publisherElectronic Transactions on Numerical Analysisru_RU
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectextended Krylovru_RU
dc.subjectIterative methodsru_RU
dc.subjectKrylovru_RU
dc.subjectrational Krylovru_RU
dc.subjectrotationsru_RU
dc.subjectsimilarity transformationsru_RU
dc.titleComputing approximate (block) rational Krylov subspaces without explicit inversion with extensions to symmetric matricesru_RU
dc.typeArticleru_RU

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