Implicitly Restarted Arnoldi Methods and Subspace Iteration

This goal of this paper is to present an elegant relationshipbetween an implicitly restarted Arnoldi method (IRAM) and nonstationary (subspace) simultaneous iteration. This relationship allows the geometric convergence theory developed for nonstationary simultaneous iteration due to Watkins and Elsner Linear Algebra Appl., 143 (1991), pp. 19--47 to be used for analyzing the rate of convergence of an IRAM. We also comment on the relationship with other restarting schemes. A set of experiments demonstrates that implicit restarted methods can converge at a much faster rate than simultaneous iteration when iterating on a subspace of equal dimension.