关键词: 鞍点, 迭代法, 对称正定矩阵, SOR-like方法, MPSOR-like方法

Abstract: A new iterative solution with undetermined parameters is proposed to solve the problem of large-scale sparse saddle point, i.e. the modified SOR-like method or MPSOR-like method. Based on a splitting for the matrix of coefficients, the iteration method needs the choices of a pretreated matrix and undetermined parameters. After the choices were done, the iteration method proposed becomes convergent in form of theorem, thus giving a basic equality between the eigenvalue of iterative matrix and the parameters, with the sufficient and necessary conditions deduced for the convergence of the iteration method. The new method shows theoretically that it is more extensive with quicker convergence rate than the SOR-like method if the parameters is chosen properly. An experimental result of the iteration method is given numerically.