关于广义区间USSOR方法和SSOR方法的收敛性的证明  

THE PROOF OF THE CONVERGENCE OF GENERAL INTERVAL USSOR METHOD AND SSOR METHOD

作　　者：滑伟[1] 

机构地区：[1]南京工程学院数理部,南京211167

出　　处：《高等学校计算数学学报》2014年第2期120-127,共8页Numerical Mathematics A Journal of Chinese Universities

基　　金：南京工程学院科研基金项目(CKJB201219)

摘　　要：1广义区间矩阵迭代的USSOR方法和SSOR方法设A∈I(R^(n×n))是一个区间矩阵,b∈I(R^n)是区间向量(见[1]).将A分解成A=D-L-U,其中D,-L和-U分别是A的对角矩阵,严格下和上三角矩阵(见[2]).假定A的每个对角元均不为零。In this paper, we considere the general interval USSOR method and SSOR method for solving linear interval equations by using the concept of companion matrix in interval matrix and scaling transformation in real matrix. The areas of the relaxation factors are discussed and some sufficient conditions for the convergence of the general interval USSOR method and SSOR method are given for the H-matrices, especially for the strictly diagonally dominant matrices. The original interval SSOR method is expanded.

关 键 词：SOR方法 广义区间 收敛性 证明 上三角矩阵 矩阵迭代 区间矩阵 对角矩阵 

分 类 号：O241.6[理学—计算数学]