NDLI: Optimal Scaling of Generalized and Polynomial Eigenvalue Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Betcke, T.
Copyright Year	2008
Abstract	Scaling is a commonly used technique for standard eigenvalue problems to improve the sensitivity of the eigenvalues. In this paper we investigate scaling for generalized and polynomial eigenvalue problems (PEPs) of arbitrary degree. It is shown that an optimal diagonal scaling of a PEP with respect to an eigenvalue can be described by the ratio of its normwise and componentwise condition number. Furthermore, the effect of linearization on optimally scaled polynomials is investigated. We introduce a generalization of the diagonal scaling by Lemonnier and Van Dooren to PEPs that is especially effective if some information about the magnitude of the wanted eigenvalues is available and also discuss variable transformations of the type $\lambda=\alpha\mu$ for PEPs of arbitrary degree.
Starting Page	1320
Ending Page	1338
Page Count	19
File Format	PDF
ISSN	08954798
DOI	10.1137/070704769
e-ISSN	10957162
Journal	SIAM Journal on Matrix Analysis and Applications (SJMAEL)
Issue Number	4
Volume Number	30
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2008-10-16
Access Restriction	Subscribed
Subject Keyword	Eigenvalues, singular values, and eigenvectors balancing scaling backward error Eigenvalues, eigenvectors polynomial eigenvalue problem condition number
Content Type	Text
Resource Type	Article
Subject	Analysis

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