On the Convergence Rate of a Preconditioned Subspace Eigensolver

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 and the relative separation of the first two eigenvalues . This means that, for example, multigrid preconditioners can be used to find eigenvalues of elliptic PDE's at a grid-independent rate. Received: March 9, 1999, revised June 23, 1999