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DEVELOPMENTS IN PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING
Edited by: B.H.V. Topping and P. Iványi
Deflation and Augmentation Techniques in Krylov Subspace Methods for the Solution of Linear Systems
O. Coulaud1, L. Giraud1, P. Ramet2 and X. Vasseur3
1Inria Bordeaux-Sud Ouest, France
O. Coulaud, L. Giraud, P. Ramet, X. Vasseur, "Deflation and Augmentation Techniques in Krylov Subspace Methods for the Solution of Linear Systems", in B.H.V. Topping and P. Iványi, (Editor), "Developments in Parallel, Distributed, Grid and Cloud Computing for Engineering", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 11, pp 249-275, 2013. doi:10.4203/csets.31.11
Keywords: augmentation, deflation, Krylov subspace methods, linear systems of equations, preconditioning.
In this chapter we present deflation and augmentation techniques that have been designed to accelerate the convergence of Krylov subspace methods for the solution of linear systems of equations. We review numerical approaches both for linear systems with a non-Hermitian coefficient matrix, mainly within the Arnoldi framework, and for Hermitian positive definite problems with the conjugate gradient method.
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