The Lanczos algorithm for the symmetric Ax = $\lambda$Bx problem.

Authors:
Gene H. Golub;Richard R. Underwood;James H. Wilkinson
Affiliations:
-;-;-
Venue:
The Lanczos algorithm for the symmetric Ax = $\'lambda$Bx problem.
Year:
1972

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Abstract

The problem of computing the eigensystem of Ax = $\lambda$Bx when A and B are symmetric and B is positive definite is considered. A generalization of the Lanczos algorithm for reducing the problem to a symmetric tridiagonal eigenproblem is given. A numerically stable variant of the algorithm is described. The new algorithm depends heavily upon the computation of elementary Hermitian matrices. An ALGOL W procedure and a numerical example are also given.