Arnoldi and Jacobi-Davidson methods for generalized eigenvalue problems $Ax=\lambda Bx$ with singular $B$

Joost Rommes
2007 Mathematics of Computation  
In many physical situations, a few specific eigenvalues of a large sparse generalized eigenvalue problem Ax = λBx are needed. If exact linear solves with A − σB are available, implicitly restarted Arnoldi with purification is a common approach for problems where B 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 B. Secondly, if exact solves are not available, Jacobi-Davidson
more » ... QZ will be presented as a robust method to compute a few specific eigenvalues. Results are illustrated by numerical experiments.
doi:10.1090/s0025-5718-07-02040-6 fatcat:6ba5air24zdo5pxrd34ouphfxy