Abstract: Some iteration methods for solving linear system were studied，when coefficient matrix is α-diagonal strictly dominance or doubly diagonal strictly dominance, and some convergence theorems were given. Results obtained were applicable to α-diagonal strictly dominance matrix or doubly diagonal strictly dominance matrix, and improved the known results and were suited to extended matrices. Finally, an numerical examples were given for illustrating advantage of results．

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

摘要： 针对线性方程组的系数矩阵为α-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。

关键词: &alpha, -严格对角占优矩阵 ,  , 双严格对角占优矩阵 , 迭代法 ,  , 收敛性