| Popis: |
We investigate the behavior of Arnoldi's method for Hermitian matrices in the case of inexact vector operations. A special purpose variant of Gram Schmidt orthogonalization is introduced which computes a nearly orthogonal Krylov subspace basis and additionally implicitly provides an exactly orthogonal basis. In the second part we perform a backward error analysis and show that the exactly orthogonal basis satisfies a Krylov relation for a perturbed system matrix. The norm of the backward error is shown to be on the level of the accuracy of the vector operations. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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