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

doi:10.12286/jssx.2020.2.223

计算数学 ›› 2020, Vol. 42 ›› Issue (2): 223-236.DOI: 10.12286/jssx.2020.2.223

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

吴敏华¹, 李郴良²

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

收稿日期:2018-10-14 出版日期:2020-05-15 发布日期:2020-05-15
通讯作者: 李郴良,Email:chenli@guet.edu.cn
基金资助:
国家自然科学基金项目（11661027）、广西自然科学基金项目资助（2015GXNSFAA139014）和国家重大仪器专项（61627807）资助.

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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.

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.

A PRECONDITIONED MODULUS-BASED MATRIX SPLITTING ITERATION METHOD FOR SOLVING THE LINEAR COMPLEMENTARITY PROBLEM WITH TOEPLITZ MATRIX

Wu Minhua¹, Li Chenliang²

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

Received:2018-10-14 Online:2020-05-15 Published:2020-05-15

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.

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

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.

Key words: modulus-based matrix iteration method, preconditioned conjugate gradient method, Toeplitz matrix, linear complementarity problems

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摘要

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

A PRECONDITIONED MODULUS-BASED MATRIX SPLITTING ITERATION METHOD FOR SOLVING THE LINEAR COMPLEMENTARITY PROBLEM WITH TOEPLITZ MATRIX

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