严格对角占优矩阵与SOR迭代法的收敛性定理

Diagonal Strictly Dominance Matrix and Convergence Theorem of SOR Iteration Method

针对线性方程组的系数矩阵为-链严格对角占优矩阵和双严格对角占优矩阵的情况,讨论了线性方程组求解时常用的SOR迭代方法的收敛性,给出了迭代法收敛性定理,解决了以往估计迭代矩阵谱半径的问题。结果不仅适用于这两类矩阵,还适用于广义严格对角占优矩阵类,最后举例说明了所给结果的优越性。

In this paper Convergence theorem of SOR iteration method for solving linear system is studied,when coefficient matrix is α-chain diagonal strictly dominance or doubly diagonal strictly dominance,and some convergence theorems are given,which solves the problem of spectral radius of iterative matrices.Results obtained are applicable for α-chain diagonal strictly dominance matrix or doubly diagonal strictly dominance matrix,and improve the known results and are applicable for generalized diagonal strictly dominance matrices.Finally,a numerical example is given for illustrating advantage of the results in this paper.