外推Gauss-Seidel迭代法的收敛性及其与H-矩阵的关系  

Convergence of Extrapolated Gauss-Seidel Iterative Method and Its Relationship with H-Matrix

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,西安710062 [2]西安理工大学应用数学系,西安710054

出　　处：《吉林大学学报（理学版）》2014年第3期413-420,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:61273311;10902062)

摘　　要：考虑外推Gauss-Seidel迭代法的收敛性及其与H-矩阵的关系,给出了外推GaussSeidel迭代法与Jacobi迭代法收敛性的关系及收敛的参数范围.利用最优尺度矩阵及M-1 N的估计量给出了H-矩阵外推Gauss-Seidel法谱半径的上界估计式,并基于外推Gauss-Seidel及Gauss-Seidel迭代法得到一般H-矩阵的等价条件.The convergence performance of the extrapolated Gauss-Seidel iterative method and its relationship with H-matrix were discussed.The convergence relationship between the extrapolated Gauss-Seidel and the Jacobi iterative methods and also the range of the extrapolated parameter when the method converges were given.The upper bound estimates for the spectral radius of the extrapolated Gauss-Seidel iterative method were obtained by using the optimally scaled matrix and the estimator of M-1 N. Meanwhile,equivalent conditions for general H-matrices based on the extrapolated Gauss-Seidel and the Gauss-Seidel iterative methods were provided.

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]