Optimizing matrix stability

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

Research output: Contribution to journalArticle

Abstract

Given an affine subspace of square matrices, we consider the problem of minimizing the spectral abscissa (the largest real part of an eigenvalue). We give an example whose optimal solution has Jordan form consisting of a single Jordan block, and we show, using nonlipschitz variational analysis, that this behaviour persists under arbitrary small perturbations to the example. Thus although matrices with nontrivial Jordan structure are rare in the space of all matrices, they appear naturally in spectral abscissa minimization.

Original languageEnglish (US)
Pages (from-to)1635-1642
Number of pages8
JournalProceedings of the American Mathematical Society
Volume129
Issue number6
StatePublished - 2001

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Abscissa
Stiffness matrix
Jordan Form
Jordan Block
Variational Analysis
Square matrix
Small Perturbations
Optimal Solution
Subspace
Eigenvalue
Arbitrary

Keywords

  • Eigenvalue optimization
  • Jordan form
  • Nonsmooth analysis
  • Spectral abscissa

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Optimizing matrix stability. / Burke, J. V.; Lewis, A. S.; Overton, M. L.

In: Proceedings of the American Mathematical Society, Vol. 129, No. 6, 2001, p. 1635-1642.

Research output: Contribution to journalArticle

Burke, JV, Lewis, AS & Overton, ML 2001, 'Optimizing matrix stability', Proceedings of the American Mathematical Society, vol. 129, no. 6, pp. 1635-1642.
Burke, J. V. ; Lewis, A. S. ; Overton, M. L. / Optimizing matrix stability. In: Proceedings of the American Mathematical Society. 2001 ; Vol. 129, No. 6. pp. 1635-1642.
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