Cluster robustness of preconditioned gradient subspace iteration eigensolvers

The paper presents convergence estimates for a class of iterative methods for solving partial generalized symmetric eigenvalue problems whereby a sequence of subspaces containing approximations to eigenvectors is generated by combining the Rayleigh–Ritz and the preconditioned steepest descent/ascent methods. The paper uses a novel approach of studying the convergence of groups of eigenvalues, rather than individual ones, to obtain new convergence estimates for this class of methods that are cluster robust, i.e. do not involve distances between computed eigenvalues.