Computing accurate eigenvalues with long Richardson and short
Lanczos runs
A. Ruhe
Department of Mathematics
Chalmers University of Technology, Goteborg
Abstract: We compute eigenvalues of very large matrices. First apply Richardson iteration with Leja shifts, as described by Calvetti and Reichel, to filter out eigenvalues outside a small region of interest. Then do a short Lanczos iteration starting at this filtered vector and get approximations to eigenvalues of interest.
The hope is that the Richardson iteration generates linearly independent vectors and that extra copies of converged eigenvectors will not turn up as fast as they do in a long Lanczos run.
Numerical examples will be demonstrated.
Authors: Sonia Gupta and Axel Ruhe.