M-矩阵线性互补问题模系多分裂迭代方法的收敛性  

Convergence of Modulus-based Multisplitting Iteration Methods for Linear Complementarity Problems with M-matrices

作　　者：张丽丽[1] 任志茹[2] 

机构地区：[1]河南财经政法大学数学与信息科学学院,郑州450046 [2]中央财经大学统计与数学学院,北京100081

出　　处：《数学学报（中文版）》2017年第4期547-556,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11301141;11301521);河南省高等学校青年骨干教师资助计划(2015GGJS-006);河南省科技攻关项目(162102310385;152102310089)

摘　　要：首先证明了M-矩阵的H-相容分裂都是正则分裂,反之不成立.这表明对于M-矩阵而言,其正则分裂包含H-相容分裂.然后针对系数矩阵为M-矩阵的线性互补问题,建立了两个收敛定理:一是模系多分裂迭代方法关于正则分裂的收敛定理;二是模系二级多分裂迭代方法关于外迭代为正则分裂和内迭代为弱正则分裂的收敛定理.For M-matrix, we prove that its H-compatible splitting is the regular split- ting, but not vice versa. This indicates that the regular splittings of M-matrix contain all H-compatible splittings. For the linear complementarity problems with M-matrices,we establish two convergence theorems： one is that of the modulus-based multisplitting iteration method with regular splittings, the other is that of the modulus-based two- stage inultisplitting iteration method with regular splittings for outer iterations and weak regular splittings for inner iterations.

关 键 词：线性互补问题 模系方法 多分裂 收敛性 

分 类 号：O241.6[理学—计算数学]