Abstract
Based on the deteriorated positive definite and skew-Hermitian splitting (DPSS) preconditioner, we develop a parameterized DPSS (PDPSS) preconditioner for the nonsymmetric saddle point linear systems. The spectral properties of the PDPSS preconditioned coefficient matrix are analyzed. Moreover, an upper bound of the degree of the minimal polynomial of the PDPSS preconditioned matrix is also obtained. Inasmuch as the efficiency of the PDPSS preconditioner depends on the values of its parameters, we further derive a fast and effective method to compute the optimal parameter values of the PDPSS preconditioner. Finally, numerical examples are employed to illustrate the feasibility and the efficiency of the PDPSS preconditioner.
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