| 求解带Toeplitz矩阵的线性互补问题的一类预处理模系矩阵分裂迭代法 |
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| 引用本文： | 吴敏华,李郴良.求解带Toeplitz矩阵的线性互补问题的一类预处理模系矩阵分裂迭代法[J].计算数学,2020,42(2):223-236. |
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| 作者姓名： | 吴敏华 李郴良 |
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| 作者单位： | 1. 广东金融学院金融数学与统计学院, 广州 510521;
2. 桂林电子科技大学数学与计算科学学院, 广西高校数据分析与计算重点实验室, 桂林 541004 |
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| 基金项目： | 重大仪器专项;广西自然科学基金;国家自然科学基金 |
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| 摘 要： | 针对系数矩阵为对称正定Toeplitz矩阵的线性互补问题，本文提出了一类预处理模系矩阵分裂迭代方法.先通过变量替换将线性互补问题转化为一类非线性方程组，然后选取Strang或T.Chan循环矩阵作为预优矩阵，利用共轭梯度法进行求解.我们分析了该方法的收敛性.数值实验表明，该方法是高效可行的.
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| 关 键 词： | 模系矩阵分裂迭代方法 预优共轭梯度法 Toeplitz矩阵 线性互补问题 |
| 收稿时间： | 2018-10-14 |
A PRECONDITIONED MODULUS-BASED MATRIX SPLITTING ITERATION METHOD FOR SOLVING THE LINEAR COMPLEMENTARITY PROBLEM WITH TOEPLITZ MATRIX |
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| Wu Minhua,Li Chenliang.A PRECONDITIONED MODULUS-BASED MATRIX SPLITTING ITERATION METHOD FOR SOLVING THE LINEAR COMPLEMENTARITY PROBLEM WITH TOEPLITZ MATRIX[J].Mathematica Numerica Sinica,2020,42(2):223-236. |
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| Authors: | Wu Minhua Li Chenliang |
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| Institution: | 1. Guangdong University of Finance School of Financial Mathematics&Statistics, Guangzhou 510521, China;
2. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China |
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| Abstract: | In this paper, a preconditioned modulus-based matrix splitting iteration method is presented for solving the linear complementarity problem with a symmetric positive-defined Toeplitz matrix. Firstly we transformed the linear complementarity problem into a nonlinear equations, then solve it by using preconditioned conjugate gradient method with Strang precondition matrix or T.Chan precondition matrix. We analyzed the convergence of the new method, and confirmed its efficiency through some numerical examples. |
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| Keywords: | modulus-based matrix iteration method preconditioned conjugate gradient method Toeplitz matrix linear complementarity problems |
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