On the Convergence Rate of a Preconditioned Subspace Eigensolver

Abstract.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.

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