TY  - JOUR
EP  - 536
IS  - 3
AV  - public
SN  - 0024-3795
TI  - Perturbation, extraction and refinement of invariant pairs for matrix polynomials
KW  - Polynomial eigenvalue problem
KW  -  Invariant pairs
KW  -  Numerical algorithm
KW  -  Perturbation theory
KW  -  QUADRATIC EIGENVALUE PROBLEMS
KW  -  NUMERICAL-SOLUTION
KW  -  SUBSPACES
KW  -  LINEARIZATIONS
KW  -  ALGORITHM
KW  -  BOUNDS
KW  -  ERROR
UR  - http://dx.doi.org/10.1016/j.laa.2010.06.029
ID  - discovery1056733
N2  - 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.
Y1  - 2011/08/01/
PB  - ELSEVIER SCIENCE INC
A1  - Betcke, T
A1  - Kressner, D
JF  - Linear Algebra and its Applications
SP  - 514
VL  - 435
ER  -