求解一类非线性互补问题的松弛two-sweep模系矩阵分裂迭代法

doi:10.12286/jssx.j2020-0660

计算数学 ›› 2021, Vol. 43 ›› Issue (1): 118-132.DOI: 10.12286/jssx.j2020-0660

• 论文 • 上一篇

求解一类非线性互补问题的松弛two-sweep模系矩阵分裂迭代法

丁戬, 殷俊锋

同济大学数学科学学院, 上海 200092

收稿日期:2020-01-09 出版日期:2021-02-15 发布日期:2021-02-04
基金资助:
本研究受到国家自然科学基金（项目号：11971354）资助.

PDF ( 217 ) 引用

丁戬, 殷俊锋. 求解一类非线性互补问题的松弛two-sweep模系矩阵分裂迭代法[J]. 计算数学, 2021, 43(1): 118-132.

Ding Jian, Yin Junfeng. THE RELAXATION TWO-SWEEP MODULUS-BASED MATRIX SPLITTING ITERATION METHODS FOR A CLASS OF NONLINEAR COMPLEMENTARITY PROBLEMS[J]. Mathematica Numerica Sinica, 2021, 43(1): 118-132.

THE RELAXATION TWO-SWEEP MODULUS-BASED MATRIX SPLITTING ITERATION METHODS FOR A CLASS OF NONLINEAR COMPLEMENTARITY PROBLEMS

Ding Jian, Yin Junfeng

School of Mathematical Sciences, Tongji University, Shanghai 200092, China

Received:2020-01-09 Online:2021-02-15 Published:2021-02-04

本文构造了求解一类非线性互补问题的松弛two-sweep模系矩阵分裂迭代法. 理论分析建立了新方法在系数矩阵为正定矩阵或H₊矩阵时的收敛性质．数值实验结果表明新方法是行之有效的, 并且在最优参数下松弛two-sweep模系矩阵分裂迭代法在迭代步数和时间上均优于传统的模系矩阵分裂迭代法和two-sweep模系矩阵分裂迭代法.

关键词： 非线性互补问题, 矩阵分裂, 松弛two-sweep模系迭代法, 正定矩阵, H₊阵

To solve a class of nonlinear complementarity problems, the relaxation modulus-based matrix splitting iteration methods are presented and analyzed. Convergence theory is established when the system matrix is a positive definite matrix or an H₊-matrix. Numerical experiments show that the proposed methods are efficient and better than the modulusbased matrix splitting iteration methods and the two-sweep modulus-based matrix splitting iteration methods in aspects of iteration steps and CPU time.

Key words: Nonlinear complementarity problems, Matrix splitting, Two-sweep modulusbased iteration methods, Positive definite matrix, H₊-matrix

MR(2010)主题分类:

65F10
65H10

分享此文:

[1] Berman A and Plemmons R J. Nonnegative Matrix in the Mathematical Sciences[M]. Academic Press, 1979.
[2] Cottle R, Pang J S, Stone R. The Linear Complementarity Problem[M]. Academic, San Diego, 1992.
[3] Ferris M C, Pang J S. Engineering and economic applications of complementarity problems[M]. Siam Review, 1997, 39:669-713.
[4] Bai Z Z. Modulus-based matrix splitting iteration methods for linear complementarity problems[J]. Numerical Linear Algebra with Applications, 2010, 17:917-933.
[5] Zhang L L. Two-step modulus based matrix splitting iteration for linear complementarity problems[J]. Numerical Algorithms, 2011, 57:83-99.
[6] Zheng N, Yin J F. Accelerated modulus-based matrix splitting iteration methods for linear complementarity problems[J]. Numerical Algorithms. 2013, 64:245-262.
[7] Wu S L. Li C X. Two-sweep modulus-based matrix splitting iteration methods for linear complementarity problems[J]. Journal of Computational and Applied Mathematics, 2016, 302:327-339.
[8] Xia Z C, Li C L. Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problem[J]. Applied Mathematics and Computation, 2015, 271:34-42.
[9] Li R, Yin J F. Accelerated modulus-based matrix splitting iteration methods for a restricted class of nonlinear complementarity problems[J]. Numerical Algorithms, 2017, 75:339-358.
[10] Huang N, Ma C F. The modulus-based matrix splitting algorithms for a class of weakly nonlinear complementarity problems[J]. Numerical Linear Algebra with Applications, 2016, 23:558-569.
[11] Huang B H, Ma C F. Accelerated modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems[J]. Computational and Applied Mathematics, 2018, 37:3053-3076.
[12] 李蕊,殷俊锋. 两步模系矩阵分裂算法求解弱非线性互补问题.同济大学学报:自然科学版[J]. 2017, 45:296-301.
[13] Peng X F, Wang M, Li W. A Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems[J]. East Asian Journal on Applied Mathematics, 2019, 9:102-121.
[14] Zheng H. Li W. Vong S W. A relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems[J]. Numerical Algorithms, 2017, 74:137-152.
[15] 李郴良,孙芳莉,黄杰彬. 一类非线性互补问题的模系矩阵分裂的Two-sweep方法.高等学校计算数学学报[J]. 2019, 41:209-223.
[16] Frommer A, Mayer G. Convergence of relaxed parallel multisplitting methods[J]. Linear Algebra and its Applications, 1989, 119:141-152.
[17] Shen S Q, Huang T Z. Convergence and comparison theorems for double splittings of matrices[J]. Computers and Mathematics with Applications, 2006, 51:1751-1760.

[1]	胡雅伶, 彭拯, 章旭, 曾玉华. 一种求解非线性互补问题的多步自适应Levenberg-Marquardt算法[J]. 计算数学, 2021, 43(3): 322-336.
[2]	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.
[3]	李枝枝, 柯艺芬, 储日升, 张怀. 二阶锥线性互补问题的广义模系矩阵分裂迭代算法[J]. 计算数学, 2019, 41(4): 395-405.
[4]	李郴良, 田兆鹤, 胡小媚. 一类弱非线性互补问题的广义模系矩阵多分裂多参数加速松弛迭代方法[J]. 计算数学, 2019, 41(1): 91-103.
[5]	郑华, 罗静. 一类H矩阵线性互补问题的预处理二步模基矩阵分裂迭代方法[J]. 计算数学, 2018, 40(1): 24-32.
[6]	温瑞萍, 孟国艳, 王川龙. 对称正定线性方程组具有任意权矩阵的多分裂迭代求解[J]. 计算数学, 2014, 36(1): 27-34.
[7]	范斌, 马昌凤, 谢亚君. 求解非线性互补问题的一类光滑Broyden-like方法[J]. 计算数学, 2013, 35(2): 181-194.
[8]	温瑞萍, 孟国艳, 关晋瑞. 非对称线性方程组的二阶段分裂迭代法[J]. 计算数学, 2012, 34(4): 405-412.
[9]	陈争, 马昌凤. 求解非线性互补问题一个新的 Jacobian 光滑化方法[J]. 计算数学, 2010, 32(4): 361-372.
[10]	屈彪,王长钰,张树霞,. 一种求解非线性互补问题的方法及其收敛性[J]. 计算数学, 2006, 28(3): 247-258.
[11]	蔡放,熊岳山,. 矩阵分裂序列与线性二级迭代法[J]. 计算数学, 2006, 28(2): 113-120.
[12]	乌力吉,陈国庆. 非线性互补问题的一种新的光滑价值函数及牛顿类算法[J]. 计算数学, 2004, 26(3): 315-328.
[13]	欧阳柏玉,佟文廷. 一类亚半正定矩阵的左右逆特征值问题(Ⅱ)[J]. 计算数学, 2002, 24(2): 189-196.
[14]	欧阳柏玉. 一类亚半正定矩阵的左右逆特征值问题[J]. 计算数学, 1998, 20(4): 345-352.

阅读次数

全文

摘要

求解一类非线性互补问题的松弛two-sweep模系矩阵分裂迭代法

THE RELAXATION TWO-SWEEP MODULUS-BASED MATRIX SPLITTING ITERATION METHODS FOR A CLASS OF NONLINEAR COMPLEMENTARITY PROBLEMS

扫码分享