M-矩阵线性方程组的一类Jacobi-Like迭代法

A Class of Jacobi-Like Iteration Method for M-Matrix Linear Systems

文章研究了M-矩阵线性方程组的求解问题.基于系数矩阵的一类预处理并利用M-矩阵的性质,得到系数矩阵的一类适当的分裂,进而提出了一类Jacobi-like迭代法以计算方程组的解.理论分析和数值实验表明,新方法是可行的,而且在一定情况下也是较为有效的.

We study the problem of solving M-matrix linear systems.Based on a kind of preconditioning of the coefficient matrix and using the properties of M-matrix,an appropriate splitting of the coefficient matrix is obtained.Then a class of Jacobi-like iterative method is proposed to solve the linear systems.Theoretical analysis and numerical experiments show that the new method is feasible and effective in some cases.