2025年5月10日 周六
首页本刊简介投稿须知编委会成员论文撰写模板论文格式要求过刊全文链接审稿单联系我们English
首页 > 过刊浏览>2019年第47卷第02期 >0291-0297. DOI:10.11908/j.issn.0253-374x.2019.02.019
PDF HTML阅读 XML下载 导出引用 引用提醒
松弛模系矩阵分裂迭代法求解一类非线性互补问题
CSTR:
[cstr]
作者:
作者单位:

同济大学数学科学学院,同济大学数学科学学院,同济大学数学科学学院

中图分类号:

O241.8

基金项目:

中央高校基本科研业务费专项资金；国家自然科学基金（11701221）


A Relaxation Modulus-based Matrix Splitting Iteration Method for a Class of Nonlinear Complementarity Problems
Author:
  • 摘要
    • | |
  • 访问统计
    • |
  • 参考文献 [20]
    • |
  • 相似文献 [20]
    • |
  • 引证文献
    • | |
  • 文章评论
    摘要:

    考虑松弛模系矩阵分裂迭代法求解一类非线性互补问题, 理论分析给出了当系数矩阵为H+矩阵时迭代法的收敛性和松弛参数的选取方法. 数值实验表明, 松弛模系矩阵分裂迭代法在迭代步数和迭代时间上均优于模系矩阵分裂迭代法.

    Abstract:

    A relaxation modulus-based matrix splitting iteration method is proposed for solving a class of nonlinear complementarity problems. The convergence theory is established when the system matrix is H+and the choice of relaxation parameters is given. Numerical examples show that the proposed methods are efficient and can accelerate the convergence performance of the modulus-based matrix splitting method with less iteration steps and CPU time.

    参考文献
    [1]Ortega J M, Rheinboldt W C. Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
    [2]Bai Z Z. Parallel nonlinear AOR method and its convergence, Computers and Mahtematics with Applications, 1996, 31 :21-31.
    [3]Ferris M C, Pang J S. Engineering and economic applications of complementarity problems. SIAM Review, 1997, 39:669–713.
    [4]Cottle R W, Pang J S, Stone R E. The Linear Complementarity Problem [M]. Academic Press, San Diego, 2009.
    [5]Bai Z Z. Modulus-based matrix splitting iteration methods for linear complementarity problems [J]. Numerical Linear Algebra with Applications, 2010, 17: 917-933.
    [6]Zhang L L. Two-step modulus-based matrix splitting iteration method for linear complementarity problems [J]. Numerical Algorithms, 2011, 57: 83-99.
    [7]Li W. A general modulus-based matrix splitting method for linear complementarity problems of -matrices [J]. Applied Mathematics Letters. 2013, 26: 1159-1164.
    [8]Zheng N, Yin J F. Accelerated modulus-based matrix splitting iteration methods for linear complementarity problems [J]. Numerical Algorithms, 2013, 64: 245-261.
    [9]Xu W W. Modified modulus-based matrix splitting iteration methods for linear complementarity problems [J]. Numerical Linear Algebra with Applications, 2015, 22: 748-760.
    [10]Li W, Zheng H. A preconditioned modulus-based iteration method for solving linear complementarity problems of -matrices, Linear and Multilinear Algebra, 2016,7: 1390-1403.
    [11]Zheng H, Li W, Vong Seakweng. A relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems, Numerical Algorithms, 2017, 74: 137-152.
    [12]Bai Z Z, Zhang L L. Modulus-based synchronous multisplitting iteration methods for linear complementarity problems [J]. Numerical Linear Algebra with Applications, 2013, 20: 425-439.
    [13]Bai Z Z, Zhang L L. Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems[J]. Numerical Algorithms, 2013, 62:59–77.
    [14]Zhang L L. Two-step modulus-based synchronous multisplitting iteration methods for linear complementarity problems[J]. Journal of Computational Mathematics. 2015, 33(1):100-112.
    [15]张丽丽. 关于线性互补问题的模系矩阵分裂迭代方法[J]. 计算数学, 2012, 34(4): 373-386.Zhang L L. On modulus-based matrix splitting iteration methods for linear complementarity problems [J]. Mathematic Numerica Sinica, 2012, 34(4): 373-386.
    [16]黎稳, 郑华. 线性互补问题的数值分析 [J]. 华南师范大学学报(自然科学版), 2015, 47(3): 1-9.Li W, Zheng H. Numerical analysis on linear complementarity problems [J]. Journal of South China Normal University, 2015, 47(3): 1-9.
    [17]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.
    [18]Li R, Yin J F. Accelerated modulus-based matrix splitting iteration methods for a class of restricted nonlinear complementarity problems, Numerical Algorithms, 2017, 75：339-358.
    [19]Hu J G. Estimates of and their applications, Mathematica Numerica Sinica 4, 1982：272-282.
    [20]Berman A, Plemmons R J. Nonnegative matrix in the mathematical science, SIAM Publisher, Philadelphia, 1994.
    引证文献
    网友评论
    网友评论
    分享到微博
    发 布
引用本文

王艳,殷俊锋,李蕊.松弛模系矩阵分裂迭代法求解一类非线性互补问题[J].同济大学学报(自然科学版),2019,47(02):0291~0297

复制
分享
文章指标
  • 点击次数:1423
  • 下载次数: 1039
  • HTML阅读次数: 841
  • 引用次数: 0
历史
  • 收稿日期:2018-04-07
  • 最后修改日期:2018-12-04
  • 录用日期:2018-09-03
  • 在线发布日期: 2019-02-28
文章二维码

您是本站第 10611188 访问者

版权所有：《同济大学学报（自然科学版）》     主管单位：教育部    主办单位：同济大学

地址：上海市四平路1239号同济大学内    邮编：200092    电话：021-65982344     E-mail：zrxb@tongji.edu.cn

本系统由北京勤云科技发展有限公司设计