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An augmented analysis of the perturbed two-sided Lanczos tridiagonalization process
Citation Link: https://doi.org/10.15480/882.1082
Publikationstyp
Preprint
Date Issued
2012-12
Sprache
English
Institut
TORE-DOI
First published in
Preprints des Institutes für Mathematik;Bericht 169
Number in series
169
We generalize an augmented rounding error result that was proven for the symmetric Lanczos process in [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2347--2359], to the two-sided (usually unsymmetric) Lanczos process for tridiagonalizing a square matrix. We extend the analysis to more general perturbations than rounding errors in order to provide tools for the analysis of inexact and related methods. The aim is to develop a deeper understanding of the behavior of all these methods. Our results take the same form as those for the symmetric Lanczos process, except for the bounds on the backward perturbation terms (the generalizations of backward rounding errors for the augmented system). In general we cannot derive tight a priori bounds for these terms as was done for the symmetric process, but a posteriori bounds are feasible, while bounds related to certain properties of matrices would be theoretically desirable.
Subjects
Lanczos-Prozess
endliche Genauigkeit
Perturbationsanalyse, Nicht-Hermitische Matrix
Verlust der Biorthogonalität
Lanczos process
finite precision
perturbation analysis, non-Hermitian matrix
Loss of bi-orthogonality
DDC Class
510: Mathematik
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