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On pseudospectra of matrix polynomials and their boundaries


Authors: Lyonell Boulton, Peter Lancaster and Panayiotis Psarrakos
Journal: Math. Comp. 77 (2008), 313-334
MSC (2000): Primary 65F15; Secondary 65F35, 93D09
DOI: https://doi.org/10.1090/S0025-5718-07-02005-4
Published electronically: May 11, 2007
MathSciNet review: 2353955
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Abstract: In the first part of this paper (Sections 2-4), the main concern is with the boundary of the pseudospectrum of a matrix polynomial and, particularly, with smoothness properties of the boundary. In the second part (Sections 5-6), results are obtained concerning the number of connected components of pseudospectra, as well as results concerning matrix polynomials with multiple eigenvalues, or the proximity to such polynomials.


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Additional Information

Lyonell Boulton
Affiliation: Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 2AS, United Kingdom

Peter Lancaster
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary AB, Canada T2N 1N4

Panayiotis Psarrakos
Affiliation: Department of Mathematics, National Technical University, Zografou Campus, 5780 Athens, Greece

DOI: https://doi.org/10.1090/S0025-5718-07-02005-4
Keywords: Matrix polynomials, perturbation of eigenvalues, singular values, pseudospectra.
Received by editor(s): April 6, 2006
Received by editor(s) in revised form: October 29, 2006
Published electronically: May 11, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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