Variational and numerical methods for symmetric matrix pencils

Peter Lancaster, Qiang ye

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


A review is presented of some recent advances in variational and numerical methods for symmetric matrix pencils A - 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.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalBulletin of the Australian Mathematical Society
Issue number1
StatePublished - Feb 1991

ASJC Scopus subject areas

  • General Mathematics


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