| 解线性互补问题的预处理加速模Gauss-Seidel迭代方法 |
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| 引用本文： | 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. DOI: 10.12286/jssx.2019.3.308 |
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| 作者姓名： | 戴平凡 李继成 白建超 |
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| 作者单位： | 三明学院信息工程学院,三明,365004;西安交通大学数学与统计学院,西安,710049;西北工业大学应用数学系,西安,710129 |
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| 基金项目： | 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. |
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| 摘 要： | 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.
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| 关 键 词： | 线性互补问题 预处理 模系Gauss-Seidel迭代方法 比较定理 |
| 收稿时间： | 2017-12-16 |
A PRECONDITIONED ACCELERATED MODULUS-BASED GAUSS-SEIDEL ITERATION METHOD FOR SOLVING LINEAR COMPLEMENTARITY PROBLEM |
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| 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. DOI: 10.12286/jssx.2019.3.308 |
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| Authors: | Dai Pingfan Li Jicheng Bai Jianchao |
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| Affiliation: | 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 |
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| Abstract: | 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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| Keywords: | Linear complementarity problems Preconditioning Modulus-based GaussSeidel iterative method Comparison theorem |
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