松弛型二级多分裂法的上松弛收敛性  

Upper convergence of relaxed two-stage multisplitting methods

作　　者：蔡放[1] 

机构地区：[1]长沙大学数学系,长沙410003

出　　处：《应用数学与计算数学学报》2015年第1期87-93,共7页Communication on Applied Mathematics and Computation

基　　金：国家高技术研究发展计划(863计划)资助项目(2009AA01Z102);湖南省自然科学基金资助项目(10JJ6009)

摘　　要：松弛型二级多分裂法是解线性代数方程组的一种并行迭代算法,其松弛因子在(0,1]区间的下松弛收敛结果是已知的.证明了松弛型二级多分裂法松弛因子大于1的上松弛收敛性,改进了有关下松弛的收敛结果.另外,对下松弛情形给出了矩阵范数意义下的一个比较定理.The relaxed two-stage multisplitting method is a parallel iterative al- gorithm for solution of linear algebraic systems. Its lower relaxation convergence of the relaxation factor belonging to the interval （0,1] is well known, whereas the up- per relaxation convergence of the relaxation factor greater than unity has not been seen. This paper shows the upper relaxation convergence of the relaxed two-stage multisplitting method, improving the results of the lower relaxation. In addition, a comparison theorem is presented under a certain matrix norm for the case of lower relaxation.

关 键 词：线性代数方程组 矩阵多分裂 二级迭代法 

分 类 号：O241.6[理学—计算数学]