| 关于JOR迭代法的收敛性质 |
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| 引用本文： | 潘朝毅.关于JOR迭代法的收敛性质[J].四川师范大学学报(自然科学版),2009,32(4). |
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| 作者姓名： | 潘朝毅 |
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| 作者单位： | 四川教育学院,数学系,四川,成都,610041 |
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| 基金项目： | 四川省教育厅自然科学重点基金( |
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| 摘 要： | 结合Jacobi矩阵的特征值,求出了JOR迭代法收敛的充要条件.对于Jacobi矩阵特征值全部为实数以及全部为纯虚数和(或)零的两种情形,分别确定了最佳松弛因子.同时证明了对一类常见的系数矩阵,最佳的JOR迭代法即为Jacobi迭代.最后给出了相关数值实例.
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| 关 键 词： | JOR迭代法 收敛性 最佳松弛因子 |
On Convergence of JOR Iteration Method |
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| PAN Chao-yi.On Convergence of JOR Iteration Method[J].Journal of Sichuan Normal University(Natural Science),2009,32(4). |
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| Authors: | PAN Chao-yi |
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| Institution: | Department of Mathematics;Sichuan College of Education;Chengdu 610041;Sichuan |
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| Abstract: | Based on the eigenvalues of Jacobi matrix,a necessary and sufficient convergence condition of JOR iteration method is derived.Under the circumstances of that all eigenvalues of Jacobi matrix are real or each eigenvalue's real part equals zero,the optimal relaxation parameter is given respectively.For a certain kind of coefficient matrix in common use of the linear systems,it is concluded that the optimal JOR method is exactly the Jacobi method.Some relevant numerical examples are given to illustrate the res... |
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| Keywords: | Jacobi |
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