Changing poles in the rational Lanczos method for the Hermitian eigenvalue problem

Abstract

Applications such as the modal analysis of structures and acoustic cavities require a number of eigenvalues and eigenvectors of large-scale Hermitian eigenvalue problems. The most popular method is probably the spectral transformation Lanczos method. An important disadvantage of this method is that a change of pole requires a complete restart. In this paper, we investigate the use of the rational Krylov method for this application. This method does not require a complete restart after a change of pole. It is shown that the change of pole can be considered as a change of Lanczos basis. The major conclusion of this paper is that the method is numerically stable when the poles are chosen in between clusters of the approximate eigenvalues. Copyright (C) 2001 John Wiley & Sons, Ltd.