A Stable Generalized Eigenvalue Problem

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1976 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Numerical Analysis, volume 13, pages 854-860 (issn: 0036-1429, eissn: 1095-7170,

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Authors: Crawford, C. R.;

doi: 10.1137/0713067

A Stable Generalized Eigenvalue Problem

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Abstract

The eigenvalue problem $Ax = \lambda Bx$ is considered where A and B are real symmetric matrices. Perturbation bounds are obtained in case the expression $(x^ * Ax)^2 + (x^ * Bx)^2 $ is bounded away from zero. Numerical methods for the solution of the problem are discussed.

Keywords

Eigenvalues, singular values, and eigenvectors

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