Evaluating non-analytic functions of matrices

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Abstract

The paper revisits the classical problem of evaluating f(A) for a real function f and a matrix A with real spectrum. The evaluation is based on expanding f in Chebyshev polynomials, and the focus of the paper is to study the convergence rates of these expansions. In particular, we derive bounds on the convergence rates which reveal the relation between the smoothness of f and the diagonalizability of the matrix A. We present several numerical examples to illustrate our analysis.

Original languageEnglish
Pages (from-to)613-636
Number of pages24
JournalJournal of Mathematical Analysis and Applications
Volume462
Issue number1
DOIs
StatePublished - 1 Jun 2018

Keywords

  • Chebyshev polynomials
  • Convergence rates
  • Jordan blocks
  • Matrix Chebyshev expansion
  • Matrix functions

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