Abstract
We present a general framework for a number of techniques based on projection methods on ‘augmented Krylov subspaces’. These methods include the deflated GMRES algorithm, an inner–outer FGMRES iteration algorithm, and the class of block Krylov methods. Augmented Krylov subspace methods often show a significant improvement in convergence rate when compared with their standard counterparts using the subspaces of the same dimension. The methods can all be implemented with a variant of the FGMRES algorithm. © 1997 by John Wiley & Sons, Ltd.
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