H-矩阵基于外推Gauss-Seidel迭代法的几个等价条件  

Several equivalent conditions for H-matrix based on the extrapolated Gauss-Seidel iterative method

作　　者：薛秋芳[1,2] 高兴宝[1] 刘晓光[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]西安理工大学理学院应用数学系,陕西西安710054

出　　处：《山东大学学报（理学版）》2013年第4期65-71,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61273311;61173094)

摘　　要：利用最优尺度矩阵及M-1N的某些估计量讨论了外推Gauss-Seidel迭代法的收敛性及其和H-矩阵的关系。基于外推Gauss-Seidel及Gauss-Seidel迭代法得到了H-矩阵的几个等价条件。同时也得到了严格对角占优矩阵,不可约对角占优矩阵及Stieltjes矩阵的Gauss-Seidel迭代法,外推Gauss-Seidel迭代法的相关收敛性结论。The optimal scaling matrix and the estimates of some amounts of M^-1 N are used to discuss the convergence of the extrapolated Gauss-Seidel iteration methods and the relationship between them and H-matrices. Several equivalent conditions for the H-matrices based on the extrapolated Gauss-Seidel and the Gauss-Seidel iterative methods are obtained. And the convergence results of the Gauss-Seidel and the extrapolated Gauss-Seidel iterative methods are given for the strictly diagonally dominant matrices, the irreducible diagonally dominant matrices and the Stieltjes matrices.

关 键 词：H-矩阵 GAUSS-SEIDEL迭代法 外推Gauss-Seidel迭代法 最优尺度矩阵 谱半径 

分 类 号：O241.6[理学—计算数学]