Arnoldi and Jacobi-Davidson methods for generalized eigenvalue problems ๐ด๐ฅ=๐๐ต๐ฅ with singular ๐ต
Joost Rommes ยท Mathematics of Computation ยท 2007
In many physical situations, a few specific eigenvalues of a large sparse generalized eigenvalue problem A x = ฮป B x Ax=\lambda Bx are needed. If exact linear solves with A โ ฯ B A-\sigma B are available, implicitly restarted Arnoldi with purification is a common approach for problems where B 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 B . 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.