28 October 1999
Dr Rich Lehoucq
We show that Sorensen's (1992) implicitly restarted Arnoldi method (IRAM) (including its block extension) is non-stationary simultaneous iteration in disguise. By using the geometric convergence theory for non-stationary simultaneous iteration due to Watkins and Elsner (1991) we prove that an implicitly restarted Arnoldi method can achieve a super-linear rate of convergence to the dominant invariant subspace of a matrix. We conclude with some numerical results the demonstrate the efficiency of IRAM.
- Computational Mathematics and Applications Seminar