On the convergence rate of a preconditioned subspace eigensolver (Q1969306)

The paper presents a proof of convergence for a preconditioned subspace method, based on a Davidson type algorithm, which shows the dependency of the convergence rate on the preconditioner used. More precisely, it is show that the convergence rate depends on the condition number of the preconditioner system and the relative separation of the first two eigenvalues. Finally it is demonstrated that, using a multigrid preconditioned conjugate gradient algorithm, for suitable discretizations of elliptic partial differential equations, the convergence rate is bounded independently of the grid spacing.