===firstname: Ron ===firstname3: ===affil6: ===lastname3: ===email: Ronald_Morgan@baylor.edu ===keyword_other2: ===lastname6: ===affil5: ===lastname4: ===lastname7: ===affil7: ===postal: Math Department Baylor University Waco, TX 76798-7328 ===ABSTRACT: We will discuss new Krylov methods for computing eigenvalues and eigenvectors. These include a multigrid method that improves by doing much of the computation on coarse grids. Also, a polynomial preconditioned Arnoldi can significantly speed up difficult eigenvalue problems. And for very difficult problems, a new method needs two iterations, but can compute eigenvectors without either restarting or saving a large subspace. ===affil3: ===title: Krylov Methods for Difficult Eigenvalue Problems ===affil2: ===lastname2: ===firstname4: ===keyword1: Eigenvalue and singular value methods and applications ===workshop: no ===lastname: Morgan ===firstname5: ===keyword2: NOT_SPECIFIED ===otherauths: ===affil4: ===competition: no ===firstname7: ===firstname6: ===keyword_other1: Krylov methods ===lastname5: ===affilother: ===firstname2: