A Note on Convergence for JOR Ite ration Method

Journal of Liaoning Petrochemical University ›› 2007, Vol. 27 ›› Issue (2): 84-86.

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A Note on Convergence for JOR Ite ration Method

School of Science , Liaoning University of Petroleum & Chemical Technology , F ushun Liaoning 113001 , P .R .China

Received:2006-10-10 Published:2007-06-20 Online:2017-07-05

关于JOR 迭代法收敛性的一个注记

路永洁, 宋岱才

辽宁石油化工大学理学院, 辽宁抚顺113001

作者简介:路永洁(1964), 女, 江苏宜兴市, 副教授, 硕士。
基金资助:
辽宁石油化工大学重点学科建设资助项目(K200409)

Abstract

Abstract:

　 According to the concept of the generalized double strictly diagonally dominant matrix , a new upper bound of spectrum radius for JOR iteration matrix and a convergence theorem of iteration method were given , aiming at commonly used iteration method while solving linear equations.The results are suitable to not only double strictly diagonal dominant matrices but also gene ralized double strictly diagonally dominant matrices.Assessment on spectrum radius of the relative iteration matrix is more exact , and the range of choosing convergent parameters of JOR is extended.An example illustrated the advantages of given results .

Key words: Convergence, , Gener alized strictly diagonal dominance, , JOR iteration, , Spectrumr adius

摘要： 　基于广义双严格对角占优的概念, 针对线性方程组在求解时常用的JOR 迭代方法, 给出了JOR 迭代矩阵谱半径新的上界及迭代法的收敛性定理。结果不仅适用于双严格对角占优矩阵, 还适用于广义双严格对角占优矩阵类, 对相应迭代矩阵谱半径的估计更精确, 且扩大了JOR 方法收敛参数的选取范围, 并用数值例子说明了所给结果的优越性。

关键词: 收敛性, 　广义双严格对角占优, 　JOR 迭代法, 　谱半径

LU Yong -jie,SONG Dai -cai. A Note on Convergence for JOR Ite ration Method[J]. Journal of Liaoning Petrochemical University, 2007, 27(2): 84-86.

路永洁, 宋岱才. 关于JOR 迭代法收敛性的一个注记[J]. 辽宁石油化工大学学报, 2007, 27(2): 84-86.

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A Note on Convergence for JOR Ite ration Method

关于JOR 迭代法收敛性的一个注记

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