A Parameterized Deteriorated PSS Preconditioner And Its Optimal Parameters For Saddle Point Problems

For saddle point problems,Pan et al.(Appl.Math.Comput 172:762-771,2006)proposed a deteriorated positive-definite and skew-Hermitian splitting(DPSS)pre-conditioner.In order to further improve the efficiency of the DPSS precondition-er,we propose a class of more flexible and efficient parameterized DPSS(PDPSS)preconditioner.The spectral properties of the PDPSS precnditioned matrix are analyzed.Moreover,an upper bound of the degree of the minimal polynomial of the PDPSS preconditioned matrix is also obtained.Since the performance of the PDPSS preconditioner depends on its parameter values,we further derive a class of fast and effective formals which are used to compute the optimal parameter values of the PDPSS preconditioner.Finally,numerical examples are employed to illustrate the feasibility and effectiveness of the PDPSS preconditioner.