DEFLATED AND AUGMENTED KRYLOV SUBSPACE TECHNIQUES

We present a general framework for a number of techniques based on pro jection methods on 'augmented Krylov subspaces'. These methods include the deflated GMRES algorithm, an inner-outer FGMRES iteration algorit hm, and the class of block Krylov methods. Augmented Krylov subspace m ethods often show a significant improvement in convergence rate when c ompared with their standard counterparts using the subspaces of the sa me dimension. The methods can all be implemented with a variant of the FGMRES algorithm. (C) 1997 by John Wiley & Sons, Ltd.