Spectral conditioning and pseudospectral growth

J. V. Burke, A. S. Lewis, M. L. Overton

Research output: Contribution to journalArticlepeer-review

Abstract

Using the language of pseudospectra, we study the behavior of matrix eigenvalues under two scales of matrix perturbation. First, we relate Lidskii's analysis of small perturbations to a recent result of Karow on the growth rate of pseudospectra. Then, considering larger perturbations, we follow recent work of Alam and Bora in characterizing the distance from a given matrix to the set of matrices with multiple eigenvalues in terms of the number of connected components of pseudospectra.

Original languageEnglish (US)
Pages (from-to)27-37
Number of pages11
JournalNumerische Mathematik
Volume107
Issue number1
DOIs
StatePublished - Jul 2007

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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