A multigrid Krylov method for eigenvalue problems.

We are interested in computing eigenvalues and eigenvectors of matrices derived from differential equations. They are often large sparse matrices, including both symmetric and non symmetric cases. Restarted Arnoldi methods are iterative methods for eigenvalue problems based on Krylov subspaces. Multigrid methods solve differential equations by taking advantage of the hierarchy of discretizations. A multigrid Krylov method is proposed by combining Arnoldi and multigrid methods. We compare the new approach with other methods, and explore the theory to explain its efficiency.