Title: On the convergence rate of a Preconditioned Subspace Eigensolver
author: S. Oliveira (oliveira@cs.uiowa.edu).

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.

Note: this paper is to appear in Computing.