新预条件下Jacobi迭代法的比较性定理  

A New Comparison Theorem for the Preconditioned Jacobi Iterative Method

作　　者：黄湧辉[1] 

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《韩山师范学院学报》2011年第3期32-36,共5页Journal of Hanshan Normal University

摘　　要：讨论了新预条件下Jacobi迭代法的收敛性.证明在严格对角占优的L-矩阵条件下,该预条件加快了Jacobi迭代法的收敛速度,而且在该预条件下Jacobi迭代法的谱半径是单调下降的.最后用数值例子验证本文得出的结论的正确性.In this paper, the convergence analysis for a new preconditioned Jacobi iterative method was discussed.If the coefficient matrix is the strictly dominant L-matrix,the convergence rate of the precondilioned Jaeobi iterative method is faster than one of the Jacobi methods.In addition,the spectral radius of this method is monotonically decreasing.Last, a numerical example is used to verify the correctness of our theoretical resuhs.

关 键 词：谱半径 预条件迭代法 严格对角占优L矩阵 收敛速度 弱正则分裂 

分 类 号：O241.6[理学—计算数学]