## Inexact Krylov subspace methods for linear systems (2002)

Citations: | 27 - 4 self |

### BibTeX

@MISC{Eshof02inexactkrylov,

author = {Jasper van den Eshof and Gerard L.G. Sleijpen},

title = {Inexact Krylov subspace methods for linear systems},

year = {2002}

}

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### OpenURL

### Abstract

There is a class of linear problems for which the computation of the matrix-vector product is very expensive since a time consuming approximation method is necessary to compute it with some prescribed relative precision. In this paper we investigate the e#ect of an approximately computed matrix-vector product on the convergence and accuracy of several Krylov subspace solvers. The obtained insight is used to tune the precision of the matrix-vector product in every iteration so that an overall e#cient process is obtained. This gives the empirical relaxation strategy of Bouras and Fraysse proposed in [2]. These strategies can lead to considerable savings over the standard approach of using a fixed relative precision for the matrix-vector product in every step. We will argue that the success of a relaxation strategy depends on the underlying way the Krylov subspace is constructed and not on the optimality properties for the residuals. Our analysis leads to an improved version of a strategy of Bouras, Fraysse, and Giraud [3] for the Conjugate Gradient method in case of Hermitian indefinite matrices.