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| 对称线性互补问题的并行Schwarz算法 | |
| 引用本文： | 曾金平,陈高洁. 对称线性互补问题的并行Schwarz算法[J]. 高等学校计算数学学报, 2007, 29(3): 193-203 |
| 作者姓名： | 曾金平 陈高洁 |
| 作者单位： | 东莞理工学院软件学院,东莞,523808;湖南大学数学与计量经济学院,长沙,410082;湖南大学数学与计量经济学院,长沙,410082 |
| 基金项目： | 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(1) Ax 6≥0,x≥0,x~T(Ax b)=0其中,A是给定的N×N实对称矩阵,b是N×1向量.目前求解该互补问题的迭代算法有很多(如Mangasarian(1977),Mangasarian,Leone (1987),Cottle(1992),曾金平,李董辉(1994)等).区域分解法以其将大问题化为若干子问 |
| 关 键 词： | 线性互补问题 实对称矩阵 Schwarz算法 并行 R^N |
| 修稿时间： | 2004-11-21 |
A PARALLEL SCHWARZ ALGORITHM FOR SOLVING SYMMETRIC LINEAR COMPLEMENTARY PROBLEMS |
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| Zeng Jinping,Chen Gaojie. A PARALLEL SCHWARZ ALGORITHM FOR SOLVING SYMMETRIC LINEAR COMPLEMENTARY PROBLEMS[J]. Numerical Mathematics A Journal of Chinese Universities, 2007, 29(3): 193-203 | |
| Authors: | Zeng Jinping Chen Gaojie |
| Affiliation: | College of Software, Dongguan University of Technology, Dongguan 523808; College of Mathematics and Econometrics, Hunan University, Changsha 410082 |
| Abstract: | A parallel Schwarz algorithm for the solution of the symmetric linear complementary problem is proposed,in which subproblems are solved by projec- tive iterative methods.By using the properties of theprojective 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 accumu- lation 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. |
| Keywords: | additive Schwarz algorithm linear complementary problem symmetric copositive matrix convergence. |
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