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- W2079301384 abstract "We introduce the framework of “abstract perturbed Krylov methods”. This is a new and unifying point of view on Krylov subspace methods based solely on the matrix equation AQ k + F k = Q k + 1 C ̲ k = Q k C k + q k + 1 c k + 1 , k e k T and the assumption that the matrix C k is unreduced Hessenberg. We give polynomial expressions relating the Ritz vectors, quasi-orthogonal residual iterates and quasi-minimal residual iterates to the starting vector q 1 and the perturbation term F k . The properties of these polynomials and similarities between them are analyzed in some detail. The results suggest the interpretation of abstract perturbed Krylov methods as additive overlay of several abstract exact Krylov methods." @default.
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- W2079301384 date "2007-07-01" @default.
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- W2079301384 title "Abstract perturbed Krylov methods" @default.
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