Golub等研究了一种带辅助预条件参数矩阵的SOR-like方法来解鞍点问题(Golub G H,Wu X,Yuan J Y.SOR-like methods for augmented systems.BIT,2001,41(1):71—85).我们用一种新的辅助预条件取法来加速该方法去解(1,1)块是对称正定M矩阵...Golub等研究了一种带辅助预条件参数矩阵的SOR-like方法来解鞍点问题(Golub G H,Wu X,Yuan J Y.SOR-like methods for augmented systems.BIT,2001,41(1):71—85).我们用一种新的辅助预条件取法来加速该方法去解(1,1)块是对称正定M矩阵的鞍点系统,数值结果显示优于Golub等提出的预条件.展开更多
The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional ...The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like （Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel ＆ Scientific Computations, 7（4）, 453-462 （1999）） and the modified sym- metric SOR-like （MSSOR-like） methods （Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational and Applied Mathematics, 228（4）, 424-433 （2009））.展开更多
基金supported by the National Natural Science Foundation of China(11301330)the Shanghai College Teachers Visiting Abroad for Advanced Study Program(B.60-A101-12-010)a Grant of"The First-Class Discipline of Universities in Shanghai"
文摘Golub等研究了一种带辅助预条件参数矩阵的SOR-like方法来解鞍点问题(Golub G H,Wu X,Yuan J Y.SOR-like methods for augmented systems.BIT,2001,41(1):71—85).我们用一种新的辅助预条件取法来加速该方法去解(1,1)块是对称正定M矩阵的鞍点系统,数值结果显示优于Golub等提出的预条件.
基金supported by the National Natural Science Foundation of China(No.10771031)the Fundamental Research Funds for Central Universities(No.090405013)
文摘The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like （Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel ＆ Scientific Computations, 7（4）, 453-462 （1999）） and the modified sym- metric SOR-like （MSSOR-like） methods （Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational and Applied Mathematics, 228（4）, 424-433 （2009））.
