Arnoldi and Jacobi-Davidson methods for generalized eigenvalue problems
Authors:
Joost Rommes.
Affiliation:
Mathematical Institute, Utrecht University, P.O. Box 80010, NL-3508 TA Utrecht, The Netherlands
Abstract:
In many physical situations, a few specific eigenvalues of a large sparse generalized eigenvalue problem are needed. If exact linear solves with are available, implicitly restarted Arnoldi with purification is a common approach for problems where is positive semidefinite. In this paper, a new approach based on implicitly restarted Arnoldi will be presented that avoids most of the problems due to the singularity of . Secondly, if exact solves are not available, Jacobi-Davidson QZ will be presented as a robust method to compute a few specific eigenvalues. Results are illustrated by numerical experiments.