摘要
结合Jacob i矩阵的特征值,求出了JOR迭代法收敛的充要条件.对于Jacob i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Jacob i迭代.最后给出了相关数值实例.
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 results.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2009年第4期462-464,共3页
Journal of Sichuan Normal University（Natural Science）
基金
四川省教育厅自然科学重点基金((07SA120))资助项目
