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Variational and numerical methods for symmetric matrix pencils

Published online by Cambridge University Press:  17 April 2009

Peter Lancaster  and
Qiang Ye
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 λA – B 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
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 1 , February 1991 , pp. 1 - 17
Copyright
Copyright © Australian Mathematical Society 1991

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