eprintid: 1056733
rev_number: 50
eprint_status: archive
userid: 608
dir: disk0/01/05/67/33
datestamp: 2011-02-14 21:21:23
lastmod: 2021-11-29 00:21:19
status_changed: 2011-02-16 15:05:01
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Betcke, T
creators_name: Kressner, D
title: Perturbation, extraction and refinement of invariant pairs for matrix polynomials
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
keywords: Polynomial eigenvalue problem, Invariant pairs, Numerical algorithm, Perturbation theory, QUADRATIC EIGENVALUE PROBLEMS, NUMERICAL-SOLUTION, SUBSPACES, LINEARIZATIONS, ALGORITHM, BOUNDS, ERROR
abstract: Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures. (C) 2010 Elsevier Inc. All rights reserved.
date: 2011-08-01
publisher: ELSEVIER SCIENCE INC
official_url: http://dx.doi.org/10.1016/j.laa.2010.06.029
vfaculties: VMPS
oa_status: green
language: eng
primo: open
primo_central: open_green
article_type_text: Article
verified: verified_batch
elements_source: Web of Science
elements_id: 290116
doi: 10.1016/j.laa.2010.06.029
lyricists_name: Betcke, Timo
lyricists_id: TBETC52
full_text_status: public
publication: Linear Algebra and its Applications
volume: 435
number: 3
pagerange: 514-536
issn: 0024-3795
citation:        Betcke, T;    Kressner, D;      (2011)    Perturbation, extraction and refinement of invariant pairs for matrix polynomials.                   Linear Algebra and its Applications , 435  (3)   pp. 514-536.    10.1016/j.laa.2010.06.029 <https://doi.org/10.1016/j.laa.2010.06.029>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1056733/2/BeKr09.pdf