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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Received: March 9, 1999, revised June 23, 1999
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Oliveira, S. On the Convergence Rate of a Preconditioned Subspace Eigensolver. Computing 63, 219–231 (1999). https://doi.org/10.1007/s006070050032
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DOI: https://doi.org/10.1007/s006070050032