Rational Lanczos Method for the Hermitian Eigenvalue Problem

摘要

Applications such as the modal anlaysis of structures and acoustic cavities require a number of eigenvalues and eigenvectors of large scale Hermitian eigenvae 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, the authors investigate the use of the rational Krylov method for this application. This method does not require a complete restart after a change of pole. The authors prove that for a specific implementation, numerical instabilities can occur when the pole is not chosen carefully. Numerical examples illustrate the theory.