Preconditioners for saddle point linear systems with highly singular blocks.
Chen Greif, Dominik Schötzau · 2006
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 denite weight matrices. If the nullity is equal to the number of constraints, the precon-ditioned matrices have precisely two distinct eigenvalues, giving rise to immediate convergence of preconditioned MINRES. Numerical examples illustrate our analytical ndings. Key words. saddle point linear systems, high nullity, augmentation, block diagonal preconditioners, Krylov subspace iterative solvers