求解一类对称正定矩阵绝对值方程的无逆动力学模型

doi:10.3969/j.issn.1005-3085.2025.04.008

工程数学学报

求解一类对称正定矩阵绝对值方程的无逆动力学模型

马昌凤¹, 曾姣艳¹, 华瑜²

1. 福州外语外贸学院大数据学院数据科学与智能计算重点实验室，福州 350202
2. 福建师范大学数学与统计学院，福州 350117

收稿日期:2022-08-21 接受日期:2023-05-31 出版日期:2025-10-15 发布日期:2025-10-15
基金资助:
国家自然科学基金 (12371378)；福建省自然科学基金 (2024J01980).

A New Inverse-free Dynamical Model for a Class of Absolute Value Equation with Symmetric Positive Definite Matrix

MA Changfeng¹, ZENG Jiaoyan¹, HUA Yu²

1. Key Laboratory of Data Science and Intelligent Computing, School of Big Data, Fuzhou University of International Studies and Trade, Fuzhou 350202

2. School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117

Received:2022-08-21 Accepted:2023-05-31 Online:2025-10-15 Published:2025-10-15
Supported by:
The National Natural Science Foundation of China (12371378); the Natural Science Foundation of Fujian Province (2024J01980).

摘要/Abstract

摘要：

建立了求解一类对称正定矩阵绝对值方程的无逆动力学模型。同时，证明了此动力学模型的平衡点是全局渐近稳定的。数值实验结果表明，新的无逆动力学模型是可行的，且与已有的五种动力学模型进行比较。从计算时间和误差进行分析，说明了所提出的无逆动力学模型是有竞争力的。

关键词: 绝对值方程, 无逆动力学模型, 收敛性分析, 数值实验

Abstract:

In this paper, a new inverse-free dynamical model is developed for a class of absolute value equation with symmetric positive definite matrix. It is also shown that the equilibrium point of this kinetic model is globally asymptotically stable. Based on the numerical experiments, the proposed inverse-free dynamical model is feasible. Meanwhile, by comparing it with the five existing kinetic models, the analysis in terms of computational time and error shows that the inverse-free dynamical model proposed in this paper is competitive.

Key words: absolute value equation, inverse-free dynamical model, convergence analysis, numerical experiments

中图分类号:

O241.7

马昌凤, 曾姣艳, 华瑜. 求解一类对称正定矩阵绝对值方程的无逆动力学模型[J]. 工程数学学报, doi: 10.3969/j.issn.1005-3085.2025.04.008.

MA Changfeng, ZENG Jiaoyan, HUA Yu. A New Inverse-free Dynamical Model for a Class of Absolute Value Equation with Symmetric Positive Definite Matrix[J]. Chinese Journal of Engineering Mathematics, doi: 10.3969/j.issn.1005-3085.2025.04.008.

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求解一类对称正定矩阵绝对值方程的无逆动力学模型

A New Inverse-free Dynamical Model for a Class of Absolute Value Equation with Symmetric Positive Definite Matrix

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