Changing poles in the rational Lanczos method for the Hermitian eigenvalue problem
Karl Meerbergen · Numerical Linear Algebra with Applications · 2000
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 © 2001 John Wiley & Sons, Ltd.