Abstract: According to several iteration methods for solving large linear system, when coefficient matrix is of α-diagonal strictly dominance, a new upper bound for the spectral radius of the iterative matrices was presented. Parameter estimation for JOR method was discussed. Results are applicable not only for α-diagonal strictly dominance, but also for generalized α-diagonal strictly dominant matrices. The known conclusion was improved. Finally, two numerical examples were given for illustrating advantage of results.

Key words: Iteration method, α-diagonal strictly dominance, Spectral radius, Convergence

摘要： 针对大型线性方程组求解时常用的几种迭代方法，对于系数矩阵[WTHX]A[WTBX]为α-严格对角占优矩阵的情况，给出了迭代矩阵谱半径新的上界，并讨论了JOR方法参数的选取范围。结果不仅适用于α-严格对角占优矩阵，还适用于广义α-严格对角占优矩阵,改进了已有结论。最后用数值例子说明了所给结果的优越性。

关键词: 迭代法, α-严格对角占优, 谱半径, 收敛性