New algorithms for computing the real structured pseudospectral abscissa and the real stability radius of large and sparse matrices

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7 Scopus citations

Abstract

We present two new algorithms for investigating the stability of large and sparse matrices subject to real perturbations. The first algorithm computes the real structured pseudospectral abscissa and is based on the algorithm for computing the pseudospectral abscissa proposed by Guglielmi and Overton [SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1166-1192]. It entails finding the rightmost eigenvalues for a sequence of large matrices, and we demonstrate that these eigenvalue problems can be solved in a robust manner by an unconventional eigenvalue solver. We also develop an algorithm for computing the real stability radius of a real and stable matrix, which utilizes a recently developed technique for detecting the loss of stability in a large dynamical system. Both algorithms are tested on large and sparse matrices.

Original languageEnglish (US)
Pages (from-to)S447-S471
JournalSIAM Journal on Scientific Computing
Volume37
Issue number5
DOIs
StatePublished - 2015
Externally publishedYes

Keywords

  • Abscissa
  • Eigenvalue
  • Lyapunov equation
  • Real structured pseudospectrum
  • Sparse matrix
  • Stability radius

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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