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

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dc.contributor.author Mach, Thomas
dc.contributor.author Pranić, Miroslav S.
dc.contributor.author Vandebril, Raf
dc.date.accessioned 2017-01-09T11:00:15Z
dc.date.available 2017-01-09T11:00:15Z
dc.date.issued 2014
dc.identifier.citation Mach, 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.uri http://nur.nu.edu.kz/handle/123456789/2228
dc.description.abstract It 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.language.iso en ru_RU
dc.publisher Electronic Transactions on Numerical Analysis ru_RU
dc.rights Attribution-NonCommercial-ShareAlike 3.0 United States *
dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/us/ *
dc.subject extended Krylov ru_RU
dc.subject Iterative methods ru_RU
dc.subject Krylov ru_RU
dc.subject rational Krylov ru_RU
dc.subject rotations ru_RU
dc.subject similarity transformations ru_RU
dc.title Computing approximate (block) rational Krylov subspaces without explicit inversion with extensions to symmetric matrices ru_RU
dc.type Article ru_RU


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