求解广义绝对值方程的积分-牛顿型迭代法

数学物理学报 ›› 2025, Vol. 45 ›› Issue (4): 1301-1310.

求解广义绝对值方程的积分-牛顿型迭代法

马昌凤¹,曾姣艳^1,^*,康靖²,谢亚君¹()

¹福州外语外贸学院大数据学院福州 350202
²福建师范大学数学与统计学院福州 350117

收稿日期:2024-10-12 修回日期:2025-03-05 出版日期:2025-08-26 发布日期:2025-08-01
通讯作者: ^*
作者简介:E-mail: xyj@fzfu.edu.cn
基金资助:
国家自然科学基金(12371378);福建省自然科学基金(2024J01980);福建省自然科学基金(2023J011127)

Integral-Newton type Iteration Method for Solving Generalized Absolute Value Equations

Ma Changfeng¹,Zeng Jiaoyan^1,^*,Kang Jing²,Xie Yajun¹()

¹School of Big Data, Fuzhou University of International Studies and Trade, Fuzhou 350202
²School of Mathematics and and Statistics, Fujian Normal University, Fuzhou 350117

Received:2024-10-12 Revised:2025-03-05 Online:2025-08-26 Published:2025-08-01
Supported by:
NSFC(12371378);NSF of Fujian Province(2024J01980);NSF of Fujian Province(2023J011127)

摘要/Abstract

摘要：

基于 Gauss-Legendre 积分或 Newton-Cotes 积分方法, 提出了求解广义绝对值方程的积分-牛顿型迭代法和改进的积分-牛顿型迭代法. 并从理论方面证明了这两个方法的收敛性条件, 数值实验验证了所提方法是可行且有效的.

关键词: 广义绝对值方程, Gauss-Legendre 积分, Newton-Cotes 积分, 积分-牛顿型迭代法, 改进积分-牛顿型迭代法

Abstract:

Based on Gauss-Legendre integral or Newton-Cotes integral method, the integral-Newton type iteration method and the improved integral-Newton type iteration method for solving the generalized absolute value equation are presented. The convergence conditions of the two methods are proved theoretically. Numerical experiments show that the proposed methods are feasible and effective.

Key words: generalized absolute value equation, Gauss-Legendre quadrature, Newton-Cotes quadrature, integral-Newton type iteration method, improved integral-Newton type iteration method

中图分类号:

O241.7

马昌凤, 曾姣艳, 康靖, 谢亚君. 求解广义绝对值方程的积分-牛顿型迭代法[J]. 数学物理学报, 2025, 45(4): 1301-1310.

Ma Changfeng, Zeng Jiaoyan, Kang Jing, Xie Yajun. Integral-Newton type Iteration Method for Solving Generalized Absolute Value Equations[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1301-1310.

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