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Title: An augmented analysis of the perturbed two-sided Lanczos tridiagonalization process
Language: English
Authors: Paige, Christopher C. 
Panayotov, Ivo 
Zemke, Jens-Peter M.  
Keywords: Lanczos-Prozess;endliche Genauigkeit;Perturbationsanalyse, Nicht-Hermitische Matrix;Verlust der Biorthogonalität;Lanczos process;finite precision;perturbation analysis, non-Hermitian matrix;Loss of bi-orthogonality
Issue Date: Dec-2012
Abstract (english): 
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.
DOI: 10.15480/882.1082
Institute: Mathematik E-10 
Document Type: Preprint
Part of Series: Preprints des Institutes für Mathematik 
Volume number: 169
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