On the Convergence Rate of a Preconditioned Subspace Eigensolver

S. Oliveira
Department of Computer Science
University of Iowa
Ames, IA


In this paper we present a proof of convergence for a preconditioned subspace method which shows the dependency of the convergence rate on the preconditioner used. This convergence rate depends only on the condition of the pre-conditioned system \( \kappa _{2}(MA) \) and the relative separation of the first two eigenvalues \( 1-\lambda _{1}/\lambda _{2} \). This means that, for example, multigrid preconditioners can be used to find eigenvalues of elliptic PDE's at a grid-independent rate.

Contributed August 6, 1999.