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1997•Numerical Linear Algebra with ApplicationsRequires access

Deflated and Augmented Krylov Subspace Techniques

Andrew Chapman, Yousef El-Mabruk Saad

Open publisher page 196 citations

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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What this paper is about

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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Available 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.

Key concepts: Krylov subspace, Mathematics, Generalized minimal residual method, Subspace topology, Applied mathematics, Algorithm, Mathematical analysis, Iterative method

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