一类垂直线性互补问题的模系矩阵分裂迭代法

数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 1246-1254.

一类垂直线性互补问题的模系矩阵分裂迭代法

温淑鸿¹(), 柯艺芬²^,^*(), 肖丽芬²(), 陈熙文²()

¹ 福州大学至诚学院数据科学与统计系福州 350002
² 福建师范大学数学与统计学院福州 350117

收稿日期:2025-01-04 修回日期:2025-10-21 出版日期:2026-06-26 发布日期:2026-06-16
通讯作者: 柯艺芬 E-mail:32642217@qq.com;keyifen@fjnu.edu.cn;1943488318@qq.com;2513758118@qq.com
作者简介:温淑鸿, E-mail:32642217@qq.com;
肖丽芬, E-mail:1943488318@qq.com;
陈熙文, E-mail:2513758118@qq.com
基金资助:
国家自然科学基金(12371378)

A Modulus-Based Matrix Splitting Iterative Method for a Class of Vertical Linear Complementarity Problems

Shuhong Wen¹(), Yifen Ke²^,^*(), Lifen Xiao²(), Xiwen Chen²()

¹ Department of Data Science and Statistics, Fuzhou University Zhicheng College, Fuzhou 350002
² School of Mathematics and Statistics, Fujian Normal University, Fuzhou 35011

Received:2025-01-04 Revised:2025-10-21 Online:2026-06-26 Published:2026-06-16
Contact: Yifen Ke E-mail:32642217@qq.com;keyifen@fjnu.edu.cn;1943488318@qq.com;2513758118@qq.com
Supported by:
NSFC(12371378)

摘要/Abstract

摘要：

借助模技巧, 将一类垂直线性互补问题转化为一个等价的非线性方程组. 在此基础上, 建立了一种新的基于模的矩阵分裂迭代法, 并对算法的收敛性进行了分析. 最后, 提供了一个数值算例, 并将所得数值结果与其它方法进行比较.

关键词: 垂直线性互补问题, 矩阵分裂, 迭代算法, 收敛性.

Abstract:

By means of the modulus technique, a class of vertical linear complementarity problems is transformed into an equivalent nonlinear equation system. On this basis, a new modulus-based matrix splitting iterative method is established, and the convergence of the proposed algorithm is analyzed. Finally, one numerical example is provided for numerical experiment and the numerical result is compared with other methods.

Key words: Lvertical linear complementarity problem, matrix splitting, iterative method, convergence.

中图分类号:

O221.2

温淑鸿, 柯艺芬, 肖丽芬, 陈熙文. 一类垂直线性互补问题的模系矩阵分裂迭代法[J]. 数学物理学报, 2026, 46(3): 1246-1254.

Shuhong Wen, Yifen Ke, Lifen Xiao, Xiwen Chen. A Modulus-Based Matrix Splitting Iterative Method for a Class of Vertical Linear Complementarity Problems[J]. Acta mathematica scientia,Series A, 2026, 46(3): 1246-1254.

图/表 4

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