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解线性互补问题的预处理加速模Gauss-Seidel迭代方法

戴平凡1, 李继成2, 白建超3   

  1. 1. 三明学院信息工程学院, 三明 365004;
    2. 西安交通大学数学与统计学院, 西安 710049;
    3. 西北工业大学应用数学系, 西安 710129
  • 收稿日期:2017-12-16 出版日期:2019-09-15 发布日期:2019-08-21
  • 基金资助:

    国家自然科学基金(11671318);福建省自然科学基金(2016J01028);福建省教育厅科技项目(JA15469)资助.

戴平凡, 李继成, 白建超. 解线性互补问题的预处理加速模Gauss-Seidel迭代方法[J]. 计算数学, 2019, 41(3): 308-319.

Dai Pingfan, Li Jicheng, Bai Jianchao. A PRECONDITIONED ACCELERATED MODULUS-BASED GAUSS-SEIDEL ITERATION METHOD FOR SOLVING LINEAR COMPLEMENTARITY PROBLEM[J]. Mathematica Numerica Sinica, 2019, 41(3): 308-319.

A PRECONDITIONED ACCELERATED MODULUS-BASED GAUSS-SEIDEL ITERATION METHOD FOR SOLVING LINEAR COMPLEMENTARITY PROBLEM

Dai Pingfan1, Li Jicheng2, Bai Jianchao3   

  1. 1. School of Information Engineering, Sanming University, Sanming 365004, China;
    2. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China;
    3. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, 710129, China
  • Received:2017-12-16 Online:2019-09-15 Published:2019-08-21
本文提出了解线性互补问题的预处理加速模系Gauss-Seidel迭代方法,当线性互补问题的系统矩阵是M-矩阵时证明了方法的收敛性,并给出了该预处理方法关于原方法的一个比较定理.数值实验显示该预处理迭代方法明显加速了原方法的收敛.
In this paper, a preconditioned accelerated modulus-based Gauss-Seidel iteration method for solving linear complementarity problem is presented. The convergence analysis on the proposed method for solving the linear complementarity problem involved with an M-matrix is given, and a comparison theorem of the preconditioned method with respect to the original method is derived. Numerical examples show that the new method improves considerably convergence rate of the original accelerated modulus-based Gauss-Seidel iteration method for solving the linear complementarity problem.

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