Abstract: For the linear equations system whose coefficient matrix is of -diagonal strictly dominance or doubly -chain diagonal strictly dominance, convergence properties of some iteration methods were studied and some convergence theorems were given, which solves the problem of spectral radius of iterative matrices. Results are applicable not only for -diagonal strictly dominance matrix or doubly diagonal strictly dominance matrices, but also for generalized strictly diagonally dominant matrices. Finally, numerical examples were given for illustrating advantage of results.

Key words: α-diagonal strictly dominance matrix, Doubly α-chain diagonal strictly dominance matrix, Iteration method, Convergence

摘要： 针对线性方程组的系数矩阵为严格α-对角占优矩阵和严格双α-链对角占优矩阵的情况，讨论了线性方程组求解时常用的几种迭代方法的收敛性，给出了迭代法收敛性定理，解决了以往讨论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。

关键词: 严格α-对角占优矩阵, 严格双α-链对角占优矩阵, 迭代法, 收敛性