Computation of generalized matrix functions

Francesca Arrigo, Michele Benzi, Caterina Fenu

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Abstract

We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel,Linear Multilinear Algebra, 1(1973), pp. 163–171]. Our algorithms are based on Gaussian quadrature and Golub–Kahan bidiagonalization. Block variants are also investigated. Numerical experiments are performed to illustrate the effectiveness and efficiency of our techniques in computing generalized matrix functions arising in the analysis of networks
Original languageEnglish
Pages (from-to)836–860
Number of pages25
JournalSIAM Journal on Matrix Analysis and Applications
Volume37
Issue number3
DOIs
Publication statusPublished - 12 Jul 2016

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Keywords

  • generalized matrix functions
  • Gauss quadrature
  • Golub–Kahan bidiagonalization
  • network communicability

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