Some history of preconditioned iterative methods for symmetric eigenvalue problems.

Andrew Knyazev
aknyazev@math.ucdenver.edu
http://math.ucdenver.edu/~aknyazev
Department of Mathematics, University of Colorado Denver
P.O. Box 173364, Campus Box 170, Denver, CO 80217-3364


Abstract

Iterative methods for symmetric eigenvalue problems are finally becoming a numerical standard for extremely large problems. In this talk we present a survey of some theoretical convergence rate estimates for such methods, derived by soviet scientists. We consider preconditioned analogs of the power method, the steepest descent/ascent method, Chebyshev's methods, and Lanczos-type methods, as well as their block variants.