Filtered Krylov-like sequence method for symmetric eigenvalue problems

In this paper, by introducing a class of filtered Krylov-like subspaces, we present the filtered Krylov-like sequence method for computing one extreme eigenvalue and the corresponding eigenvector of symmetric matrices. The filtered Krylov-like sequence method can be desired to behave, practically, more effective and robust than the standard Krylov subspace method. We specifically select two kinds of polynomial filters, and relate them to some well-known methods. Some numerical experiments are carried out to demonstrate the convergence properties and the competitiveness of the new method.