WWW: http://math.ucdenver.edu/~aknyazev
Department of Mathematics, University of Colorado Denver
P.O. Box 173364, Campus Box 170, Denver, CO 80217-3364.
Street Address: 1250 14th Str. Room 644, Denver CO 80202
Phone: (303) 556-8442. Fax: (303) 556-8550
Email: aknyazev@math.ucdenver.edu
 
Preconditioned eigensolvers by Andrew Knyazev
 

We give a formal definition of preconditioned eigensolvers as polynomial methods. We present a survey of some theoretical convergence rate estimates for preconditioned iterative methods for symmetric eigenvalue problems. We consider preconditioned analogs of the power method, the steepest descent/ascent method, the Lanczos-type methods by Scott and Davidson, the conjugate gradient methods, as well as their block variants. We discuss possible approaches for deriving formulas of the methods and conclude that different approaches lead to the same methods.

The talk is based on the paper: "Preconditioned eigensolvers - an oxymoron?" , ETNA, 7 (1998), pp. 104-123.
 
 

International Symposium on Theory and Algorithms
for Large Scale Matrix Problems ,
August 2-5, 1998 Dalian University of Technology, Dalian, China