Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.1082
Fulltext available Open Access
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
Part of Series: Preprints des Institutes für Mathematik 
Volume number: 169
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.
URI: http://tubdok.tub.tuhh.de/handle/11420/1084
DOI: 10.15480/882.1082
Institute: Mathematik E-10 
Type: Preprint (Vorabdruck)
License: http://doku.b.tu-harburg.de/doku/lic_mit_pod.php
Appears in Collections:Publications with fulltext

Files in This Item:
File Description SizeFormat
Bericht169.pdf312,52 kBAdobe PDFThumbnail
View/Open
Show full item record

Page view(s)

290
Last Week
0
Last month
6
checked on Sep 22, 2020

Download(s)

128
checked on Sep 22, 2020

Google ScholarTM

Check

Note about this record

Export

Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.