对称线性互补问题的并行Schwarz算法  

A PARALLEL SCHWARZ ALGORITHM FOR SOLVING SYMMETRIC LINEAR COMPLEMENTARY PROBLEMS

作　　者：曾金平[1] 陈高洁[2] 

机构地区：[1]东莞理工学院软件学院,东莞523808 [2]湖南大学数学与计量经济学院,长沙410082

出　　处：《高等学校计算数学学报》2007年第3期193-203,共11页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金项目(10671060);博士点基金资助(20020532006).

摘　　要：1引言 考虑对称线性互补问题：求x∈R^N使得 Ax＋b≥0，x≥0，x^T（Ax＋b）=0，（1） 其中，A是给定的N×N实对称矩阵，b是N×1向量．A parallel Schwarz algorithm for the solution of the symmetric linear complementary problem is proposed, in which subproblems are solved by projective iterative methods. By using the properties of the projective iterative operator and the convergence of the projective iterative methods, it is shown that under some conditions any accumulation point of the iterates generated by the algorithm solves the linear complementary problem. Moreover, the existence of an accumulation point is guaranteed when the matrix is strict copositive or copositive plus. In addition, a special case is given to show that the convergence condition could be satisfied.

关 键 词：线性互补问题 实对称矩阵 SCHWARZ算法 并行 R^N 

分 类 号：O221[理学—运筹学与控制论]