H-矩阵非线性互补问题基于模的矩阵分裂迭代法改进的收敛性定理

数学物理学报 ›› 2022, Vol. 42 ›› Issue (2): 583-593.

H-矩阵非线性互补问题基于模的矩阵分裂迭代法改进的收敛性定理

马昌凤^1,*(),马飞洋²

¹ 福州外语外贸学院大数据学院福州 350202
² 北京大学信息科学与技术学院北京 100091

收稿日期:2021-01-29 出版日期:2022-04-26 发布日期:2022-04-18
通讯作者: 马昌凤 E-mail:macf@fjnu.edu.cn
基金资助:
国家自然科学基金(11901098);福建省自然科学基金(2020J05034);国家重点研发计划资助项目(2019YFC03120003)

The Improved Convergence Theorems of Modulus-Based Matrix Splitting Iteration Methods for a Class of Nonlinear Complementarity Problems with H-Matrices

Changfeng Ma^1,*(),Feiyang Ma²

¹ School of Big Data, Fuzhou University of International Studies and Trade, Fuzhou 350202
² School of Electronics Engineering and Computer Science, Peking University, Beijing 100091

Received:2021-01-29 Online:2022-04-26 Published:2022-04-18
Contact: Changfeng Ma E-mail:macf@fjnu.edu.cn
Supported by:
the NSFC(11901098);the NSF of Fujian Province(2020J05034);the Projects Funded by the National Key Research and Development Plan(2019YFC03120003)

摘要/Abstract

摘要：

该文在较弱的条件下, 证明了解一类$H$ -矩阵非线性互补问题基于模的矩阵分裂迭代法和相应的加速迭代法的收敛性定理. 这意味着对于分裂$A=M-N$有更多的选择, 使得基于模的矩阵分裂迭代法得以收敛. 改进的收敛性定理扩展了基于模的矩阵分裂迭代法的应用范围.

关键词: 非线性互补问题, 基于模的矩阵分裂迭代法, $H$-矩阵, 收敛性定理

Abstract:

In this paper, we proved the convergence theories of the modulus-based matrix splitting iteration methods and the corresponding acceleration method for nonlinear complementarity problems of $H$-matrices in a weaker condition. It implies that we have more choices for the splitting $A=M-N$ which makes the modulus-based matrix splitting iteration methods converge. The improved convergence theories extend the scope of modulus-based matrix splitting iteration methods in applications.

Key words: Nonlinear complementarity problem, Modulus-based matrix splitting iteration method, $H$-matrix, Convergence theorem

中图分类号:

O241

马昌凤,马飞洋. H-矩阵非线性互补问题基于模的矩阵分裂迭代法改进的收敛性定理[J]. 数学物理学报, 2022, 42(2): 583-593.

Changfeng Ma,Feiyang Ma. The Improved Convergence Theorems of Modulus-Based Matrix Splitting Iteration Methods for a Class of Nonlinear Complementarity Problems with H-Matrices[J]. Acta mathematica scientia,Series A, 2022, 42(2): 583-593.

图/表 2

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非线性函数	Iter	CPU	Res
$\phi_1(z)$	26	0.0010	8.5203e-006
$\phi_2(z)$	26	0.0010	8.0783e-006
$\phi_3(z)$	27	0.0010	7.0378e-006
$\phi_4(z)$	24	0.0001	8.9217e-006
$\phi_5(z)$	27	0.0370	6.7821e-006

$n$	情形1:			情形2:
	Iter	CPU	Res	Iter	CPU	Res
$20$	26	0.0010	8.5203e-006	26	0.0010	8.5203e-006
$40$	26	0.0010	8.0783e-006	26	0.0010	8.5203e-006
$60$	27	0.0010	7.0378e-006	26	0.0010	8.5203e-006
$80$	24	0.0001	8.9217e-006	26	0.0010	8.5203e-006
$200$	27	0.0370	6.7821e-006	26	0.0010	8.5203e-006