Backward error analysis of an inexact Arnoldi method
Ute Kandler, Christian A. Schröder · PAMM · 2013
Abstract 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)