A NEW PARAMETERIZED MATRIX SPLITTING PRECONDITIONER FOR THE SADDLE POINT PROBLEMS

Recently, Zheng and Lu [<i>International Journal of Computer Mathematics</i>, 96(1): 1-17, DOI: <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://dx.doi.org/10.1080/00207160.2017.1420179">10.1080/00207160.2017.1420179</ext-link>] constructed a parameterized matrix splitting (PMS) preconditioner for the large sparse saddle point problems, and gave the corresponding theoretical analysis and numerical experiments. In this paper, based on the parameterized matrix splitting, we generalize the PMS algorithms and further present the new parameterized matrix splitting (NPMS) preconditioner for the saddle point problems. Moreover, by similar theoretical analysis, we analyze the convergence conditions of the corresponding matrix splitting iteration methods and preconditioning properties of the NPMS preconditioned saddle point matrices. Finally, one example is provided to confirm the effectiveness.