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In this paper, we propose a preconditioner based on the shift-splittingmethod for generalized saddle point problems with nonsymmetric positivedefinite (1,1)-block and symmetric positive semidefinite $(2,2)$-block. Theproposed preconditioner is obtained from an basic iterative method which isunconditionally convergent. We also present a relaxed version of the proposedmethod. Some numerical experiments are presented to show the effectiveness ofthe method.

A preconditioner based on the shift-splitting method for generalized saddle point problems