On the Convergence Rate of a Preconditioned Subspace Eigensolver

摘要

In this paperwe present a proofof convergence for a preconditioned subspace methob which shows the dependencyof the convergence rate on the preconditioner used. This convergence rate depends only on the condition of the pre-conditioned system k_2(M A) and the relative separation of the first two eigenvalues1-λ1/ λ2. This means that, for example, multigrib preconditioners can be used to find eigenvalues of elliptic PDE's at a grid-independent rate.