α-严格对角占优矩阵与SOR迭代法的收敛性定理

α-Diagonal Strictly Dominance Matrix and Convergence Theorem of SOR Iteration Method

针对线性方程组的系数矩阵为α-严格对角占优矩阵和双α-链严格对角占优矩阵的情况,讨论了线性方程组求解时常用到的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α-严格对角占优矩阵类。最后举例说明了所给结果的优越性。

For the linear equations system whose coefficient matrix is of α-diagonal strictly dominance or doubly α-chain diagonal strictly dominance,convergence properties of SOR iteration method are studied and some convergence theorems are given,which solves the problem of spectral radius of iterative matrices.Results obtained are applicable not only for α-diagonal strictly dominance matrix or doubly α-chain diagonal strictly dominance matrix,but also for generalized α-diagonal strictly dominance matrices.Finally,a numerical example is given for illustrating advantage of results.