Nested Lanczos: implicitly restarting an unsymmetric Lanczos algorithm

Abstract

In this text, we present a generalization of the idea of the Implicitly Restarted Arnoldi method to the unsymmetric Lanczos algorithm, using the two-sided Gram-Schmidt process or using a full Lanczos tridiagonalization. The resulting implicitly restarted Lanczos method is called Nested Lanczos. Nested Lanczos can be combined with an implicit filter. It can also be used in case of breakdown and offers an alternative for look-ahead.