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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (12): 55-65.doi: 10.6040/j.issn.1671-9352.0.2024.213

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求解隐式互补问题的模系矩阵分裂迭代方法

温淑鸿1,柯艺芬2*,黎科良2   

  1. 1.福州大学至诚学院数据科学与统计系, 福建 福州 350002;2.福建师范大学数学与统计学院, 福建 福州 350117
  • 发布日期:2025-12-10
  • 通讯作者: 柯艺芬(1989— ),女,副教授,博士,研究方向为数值代数及其应用. E-mail:keyifen@fjnu.edu.cn
  • 作者简介:温淑鸿(1982— ),女,副教授,研究方向为数值代数及其应用. E-mail:wendywenshuhong@163.com*通信作者:柯艺芬(1989— ),女,副教授,博士,研究方向为数值代数及其应用. E-mail:keyifen@fjnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11901098,12371378,62105064);福建省自然科学基金资助项目(2023J011127,2023J01955)

Modulus-based matrix splitting iteration method for the implicit complementarity problem

WEN Shuhong1, KE Yifen2*, LI Keliang2   

  1. 1. Department of Data Science and Statistics, Fuzhou University Zhicheng College, Fuzhou 350002, Fujian, China;
    2. School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, Fujian, China
  • Published:2025-12-10

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摘要： 提出一种新的模系矩阵分裂迭代法求解隐式互补问题,该方法不依赖于初始向量的选择,且在每一迭代步中只需求解一个线性方程组。特别地,当系统矩阵是H+-矩阵时, 给出算法全局收敛的充分条件。数值实验表明所提出的新方法相比于现有的方法具有更好的数值性能。

关键词: 隐式互补问题, 基于模系方法, 收敛性

Abstract: A new modulus-based matrix splitting iteration method is mainly established for a class of implicit complementarity problem in this paper. Any specificity of the initial vector is not depended on by the proposed method, and only one linear system needs to be solved at each iteration step. In particular, when the system matrix is a H+-matrix, the sufficient conditions for global convergence are given. Numerical experiments are presented to show the efficiency of the proposed method,which is superior to the modified modulus-based matrix splitting iteration method in terms of numerical performances.

Key words: implicit complementarity problem, modulus-based method, convergence

中图分类号: 

  • O241
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