Spectral conditioning and pseudospectral growth

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

Research output: Contribution to journalArticle

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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