改进的高斯-赛德尔迭代法的收敛性分析  

The Convergence Analysis for the Preconditioned Gauss-Seidel 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：《西昌学院学报（自然科学版）》2011年第1期15-17,共3页Journal of Xichang University(Natural Science Edition)

摘　　要：本文讨论了改进的高斯-赛德尔迭代法的收敛性。在严格对角占优的L-矩阵条件下,该预条件加快了高斯-赛德尔迭代法的收敛速度,而且在该预条件下高斯-赛德尔迭代法的谱半径是单调下降的。最后用数值例子说明本文得出的结论。In this papert,he convergence analysis for a new preconditioned Gauss-Seidel iterative method was discussed.If the matrix is the strictly dominant L-matrixt,he convergence rate of the preconditioned Gauss-Seidel iterative method is faster than one of the original one.Furthermore,the spectral radius of the reconditioned Gauss-Seidel iterative method is monotonically decreasing.At last,an example was given to confirm the fact that the preconditioned Gauss-Seidel iterative method is better than the original one.

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

分 类 号：O241.6[理学—计算数学]