A Convergence proof of an Iterative Subspace Method for Eigenvalues Problems

The generalized Davidson algorithm can be seen as a method which uses preconditioned residuals to create a subspace where it is easier to find the smallest eigenvalue and its eigenvector. In this paper theoretical results proving convergence rates are shown. In addition, we investigate the use of multigrid as a preconditioner for this method and describe a new algorithm for calculating some other eigenvalue-eigenvector pairs as well, while avoiding problems of misconvergence. The advantages of implicit restarts are also investigated.