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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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A pseudospectral mapping theorem
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by S.-H. Lui;
Math. Comp. 72 (2003), 1841-1854
DOI: https://doi.org/10.1090/S0025-5718-03-01542-4
Published electronically: May 20, 2003

Abstract:

The pseudospectrum has become an important quantity for analyzing stability of nonnormal systems. In this paper, we prove a mapping theorem for pseudospectra, extending an earlier result of Trefethen. Our result consists of two relations that are sharp and contains the spectral mapping theorem as a special case. Necessary and sufficient conditions for these relations to collapse to an equality are demonstrated. The theory is valid for bounded linear operators on Banach spaces. For normal matrices, a special version of the pseudospectral mapping theorem is also shown to be sharp. Some numerical examples illustrate the theory.
References
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Bibliographic Information
  • S.-H. Lui
  • Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
  • Email: luish@cc.umanitoba.ca
  • Received by editor(s): October 11, 2001
  • Received by editor(s) in revised form: March 29, 2002
  • Published electronically: May 20, 2003
  • Additional Notes: This work was supported in part by a grant from NSERC
  • © Copyright 2003 American Mathematical Society
  • Journal: Math. Comp. 72 (2003), 1841-1854
  • MSC (2000): Primary 15A18, 15A60, 65F15
  • DOI: https://doi.org/10.1090/S0025-5718-03-01542-4
  • MathSciNet review: 1986807