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Variational and numerical methods for symmetric matrix pencils

Published online by Cambridge University Press:  17 April 2009

Peter Lancaster
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, CanadaT2N 1N4
Qiang Ye
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, CanadaT2N 1N4
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Abstract

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A review is presented of some recent advances in variational and numerical methods for symmetric matrix pencils λAB in which A is nonsingular, A and B are hermitian, but neither is definite. The topics covered include minimax and maximin characterisations of eigenvalues, perturbation by semidefinite matrices and interlacing properties of real eigenvalues, Rayleigh quotient algorithms and their convergence properties, Rayleigh-Ritz methods employing Krylov subspaces, and a generalised Lanczos algorithm.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1991

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