Volume 22, pp. 114-121, 2006.

Preconditioners for saddle point linear systems with highly singular (1,1) blocks

Chen Greif and Dominik Schötzau

Abstract

We introduce a new preconditioning technique for the iterative solution of saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioners are block diagonal and are based on augmentation, using symmetric positive definite weight matrices. If the nullity is equal to the number of constraints, the preconditioned matrices have precisely two distinct eigenvalues, giving rise to immediate convergence of preconditioned MINRES. Numerical examples illustrate our analytical findings.

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Key words

saddle point linear systems, high nullity, augmentation, block diagonal preconditioners, Krylov subspace iterative solvers

AMS subject classifications

65F10

ETNA articles which cite this article

Vol. 37 (2010), pp. 202-213 Valeria Simoncini: On a non-stagnation condition for GMRES and application to saddle point matrices

Vol. 37 (2010), pp. 307-320 Chen Greif and Michael L. Overton: An analysis of low-rank modifications of preconditioners for saddle point systems

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