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Electronic Transactions on Numerical Analysis.

Volume 38, pp. 168-183, 2011.

Copyright2011, Kent State University.

ISSN 1068-9613.

ETNA

Kent State University http://etna.math.kent.edu

PSEUDOSPECTRAL MAPPING THEOREM II

S. H. LUIy

Abstract. The pseudospectrum has become an important quantity for analyzing stability of non-normal systems.

This paper is a continuation of an earlier paper of this author where a mapping theorem for pseudospectra was given, generalizing the spectral mapping theorem for eigenvalues. The main contribution of this paper consists of asymptotic expansions of quantities which determine the sizes of components of pseudospectral sets. As an application of this theory, we solve the eigenvalue perturbation problem for an analytic function of a matrix. Some numerical examples illustrate the theory.

Key words. Eigenvalues, pseudospectra, spectral mapping theorem, condition number, eigenvalue perturbation of function of matrices

AMS subject classifications. 15A18, 15A60, 65F15

Received July 26, 2010. Accepted for publication May 5, 2011. Published online June 14, 2011. Recommended by F. Dopico. This work was in part supported by a grant from NSERC.

yDepartment of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 ([email protected]).

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