文档详情

严格对角占优矩阵与SOR迭代法的收敛性定理.pdf

发布:2017-12-13约1.32万字共3页下载文档
文本预览下载声明
第34卷第1期 长春理工大学学报(自然科学版) Vol.34 No. 1 20 11年3月 Journal of Changchun University of Science and Technology (Natural Science Edition) Mar. 2011 严格对角占优矩阵与SOR 迭代法的收敛性定理 宋岱才,敬长红,陈德艳 (辽宁石油化工大学 理学院,抚顺 113001) 摘 要:针对线性方程组的系数矩阵为 -链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: -链严格对角占优矩阵;双严格对角占优矩阵;迭代法;收敛性 中图分类号:O24 1.6;O151.2 文献标识码:A 文章编号:1672-9870 (20 11)01-0 170-03 Diagonal Strictly Dominance Matrix and Convergence Theorem of SOR Iteration Method SONG Daicai ,JING Changhong,CHEN Deyan (School of Sciences,Liaoning University of Petroleum Chemical Technology ,Fushun 11300 1) Abstract :In this paper Convergence theorem of SOR iteration method for solving linear system is studied,when coefficient ma- trix is -chain diagonal strictly dominance or doubly diagonal strictly dominance,and some convergence theorems are given , which solves the problem of spectral radius of iterative matrices. Results obtained are applicable for - chain diagonal strictly domi- nance matrix or doubly diagonal strictly dominance matrix ,and improve the known results and are applicable for generalized di- agonal strictly dominance matrices.Finally ,a numerical example is given for illustrating advantage of the results in this paper. Key words : -chain diagonal strictly dominance matrix ;doubly diagonal strictly dominance matrix ;iteration method ; convergence theorem 界限问题。最后举例说明这一结果的适用性。 1 基本概念及引理 设方程组的系数矩阵A 分解为 = ,其 n×n 中D=diag ( , ,…,
显示全部
相似文档