A generalized Jacobi-Davidson iteration method for linear eigenvalue problems

Abstract

In this paper we propose a new method for the iterative computation of a few of the extremal eigenvalues of a symmetric matrix and their associated eigenvectors. The method is based on an old and almost unknown method of Jacobi. Jacobi's approach, combined with Davidson's method, leads to a new method that has improved convergence properties and that may be used for general matrices We also propose a variant of the new method that may be useful for the computation of nonextremal eigenvalues as well.