Report Number: CS-TR-72-270
Institution: Stanford University, Department of Computer Science
Title: The Lanczos algorithm for the symmetric Ax = $\lambda$Bx
Author: Golub, Gene H.
Author: Underwood, Richard R.
Author: Wilkinson, James H.
Date: March 1972
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.