Solution of Linear Generalized Eigenvalue Problems Containing Singular Matrices

1 December 1978

journal article
research article
Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics

Vol. 22 (4) , 401-410
https://doi.org/10.1093/imamat/22.4.401

Abstract

A general method is presented for the solution of the linear generalized eigenvalue problem Ax = λBx, where matrices A and B may both be singular but ‖A — λB‖ ≢ 0. The procedure can easily be implemented on a digital computer using a Gaussian elimination algorithm with pivoting together with a QR eigensolution package. Results are given for two problems with sensitive eigenvalues.

Keywords

EIGENVALUE PROBLEMS
SINGULAR MATRICES
CONTAINING SINGULAR
GENERALIZED EIGENVALUE
PROBLEMS CONTAINING
SOLUTION OF LINEAR
LINEAR GENERALIZED

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