• 论文 •

### 解线性互补问题的并行交替迭代算法

1. 1. 广东科学技术职业学院计算机工程技术学院, 广东珠海 519090;
2. 合肥工业大学理学院, 合肥 230009
• 收稿日期:2010-05-25 出版日期:2011-09-15 发布日期:2011-09-03
• 基金资助:

广东省自然科学基金资助项目(8151064007000004).

Duan Banxiang, Zhu Xiaoping, Zhang Aiping. PARALLEL ALTERNATING ITERATIVE ALGORITHM FOR LINEAR COMPLEMENTARITY PROBLEM[J]. Journal of Numerical Methods and Computer Applications, 2011, 32(3): 183-195.

### PARALLEL ALTERNATING ITERATIVE ALGORITHM FOR LINEAR COMPLEMENTARITY PROBLEM

Duan Banxiang1, Zhu Xiaoping1, Zhang Aiping2

1. 1. College of Computer Engineering and Technology, Guangdong Vocational Institute of Science and Technology, Zhuhai 519090, Guangdong, China;
2. School of Sciences, Heifei University of Technology, Hefei 230009, China
• Received:2010-05-25 Online:2011-09-15 Published:2011-09-03

By combining Alternating Iterative Algorithm and Parallel Multi-splitting, the authors first set up Parallel Alternating Iterative Algorithm for solving the linear complementarity problem. It is shown that when the multisplittings of matrix are weak nonnegative of the first type or the second type, both models lead to convergent schemes. And then, when the multisplittings are P-regular, they establish the global convergence theory of the algorithm. The algorithm has less computational complexity and quicker velocity and is especially suitable for parallel computation of large-scale problem. The numerical experiments show the efficiency of the algorithm.

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 [1] O'Leary D P and White R E. Multi-splittings of matrix and parallel solution of linear systems[J]. SIAM J. Algebraic Discrete Methods, 1985, 6: 630-640. [2] Frommer A and Mayer G. Convergence of Relaxed Parallel Multisplitting Methods[J]. Linear Algebra and Its Applications, 1989, 119: 141-152. [3] Wang D. On the convergence of the parallel multisplitting AOR algorithm[J]. Linear Algebra and Its Applications, 1991, 154/156: 473-486. [4] Nabben R. A note on comparison theorems for splittings and multisplittings of Hermitian positive definitematrices[J]. Linear Algebra and Its Applications, 1996, 233: 67-80. [5] Elsner L. Comparisons of weak regular splittings and multisplitting methods[J]. Numerische Mathematik, 1989, 56: 283-289. [6] Climent J J, Perea C, Tortosa L. Convergence theorems for parallel alternating iterative methods[J]. Applied Mathematics and Computation, 2004, 148: 497-517. [7] 陈景良, 陈向晖. 特殊矩阵[M]. 北京: 清华大学出版社, 2001. [8] Frommer A and Szyld D B. H-splittings and two stage iterative methods[J]. Numer Math, 1992, 63: 345-356. [9] Bai Z Z and Huang T Z. Accelerated overrelaxation methods for solving linear complementarity problem[J]. J.UEST China, 1994, 23: 428-432. [10] Woznicki Z I. Nonnegative splitting theory[J]. Japan Journal on Industrial and Applied Mathematics, 1994, 11: 289-342. [11] Cottle R W , Pang J S and Stone R E. The Linear Complementarity Problem[M]. Academic Press, San Diedo, 1992. [12] Frommer A, Szyld D B. Weighted max norms, splittings, and overlapping additive Schwarz iterations[J]. Numerische Mathematik, 1999, 49: 259-278.
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