Block GMRES with Deflation of Eigenvalues Ron Morgan

Department of Mathematics, Baylor University, Waco, TX 76798-7328
Abstract Block iterative methods for solving large nonsymmetric systems of linear equations will be discussed. Block-GMRES will be modified by deflating eigenvalues and compared with other block approaches. A full orthogonalization method such as Block GMRES may have to be restarted frequently if there are limits on the storage or if orthogonalization costs are significant compared to the cost of matrix-vector products. Frequent restarting can strongly impair performance. However, sometimes this problem can be fixed by deflating eigenvalues. Approximate eigenvectors are computed at the same time that the linear equations are solved, and they are used to augment the block Krylov subspace. This deflates eigenvalues and can sometimes make the problem easy enough that small Krylov subspaces are effective. Deflation makes block-GMRES more competitive with nonrestarted methods such as block QMR.