α—严格对角占优矩阵与迭代法的收敛性定理  

α-Diagonal Strictly Dominance Matrix and Convergence Theorem of Iteration Methods

作　　者：宋岱才[1] 魏晓丽[1] 赵晓颖[1] 

机构地区：[1]辽宁石油化工大学理学院,辽宁抚顺113001

出　　处：《辽宁石油化工大学学报》2010年第1期81-83,95,共4页Journal of Liaoning Petrochemical University

基　　金：辽宁省教育厅高校科研项目(2004F100);辽宁石油化工大学重点学科建设资助项目(K200409)

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。Some iteration methods for solving linear system were studied,when coefficient matrix isα--diagonal strictly dominance or doubly diagonal strictly dominance,and some convergence theorems were given.Results obtained were applicable toα-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.

关 键 词：α-严格对角占优矩阵 双严格对角占优矩阵 迭代法 收敛性 

分 类 号：O241.6[理学—计算数学] O151.2[理学—数学]