Backward error analysis of an inexact Arnoldi method | Zendy

Kandler Ute | Zendy; Schröder Christian | Zendy

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Backward error analysis of an inexact Arnoldi method

Author(s) -

Kandler Ute,

Schröder Christian

Publication year - 2013

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.201310204

Subject(s) - orthogonalization , krylov subspace , basis (linear algebra) , generalized minimal residual method , hermitian matrix , mathematics , orthogonal basis , norm (philosophy) , arnoldi iteration , matrix (chemical analysis) , matrix norm , algorithm , eigenvalues and eigenvectors , pure mathematics , iterative method , physics , geometry , materials science , quantum mechanics , political science , law , composite material

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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