On the Alternative SOR-like Iteration Method for Solving Absolute Value Equations

被引：5
作者：
Zhang, Yiming [1 ]
Yu, Dongmei [1 ]
Yuan, Yifei [1 ]
机构：
[1] Liaoning Tech Univ, Inst Optimizat & Decis Analyt, Fuxin 123000, Peoples R China
来源：
SYMMETRY-BASEL | 2023年 / 15卷 / 03期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
absolute value equations; alternative; SOR-like method; convergence analysis; GENERALIZED NEWTON METHOD; LEVENBERG-MARQUARDT METHOD; SMOOTHING FUNCTIONS; SYSTEM; MODEL;
D O I：
10.3390/sym15030589
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, by equivalently reformulating the absolute value equation (AVE) into an alternative two-by-two block nonlinear equation, we put forward an alternative SOR-like (ASOR-like) iteration method to solve the AVE. The convergence of the ASOR-like iteration method is established, subjecting to specific restrictions placed on the associated parameter. The selection of the optimal iteration parameter is investigated theoretically. Numerical experiments are given to validate the feasibility and effectiveness of the ASOR-like iteration method.
引用
收藏
页数：17
相关论文
共 51 条
[1]   Modulus-based matrix splitting iteration methods for linear complementarity problems [J].
Bai, Zhong-Zhi .
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2010, 17 (06) :917-933
[2]   On the global convergence of the inexact semi-smooth Newton method for absolute value equation [J].
Bello Cruz, J. Y. ;
Ferreira, O. P. ;
Prudente, L. F. .
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2016, 65 (01) :93-108
[3]  
BERMAN A., 1979, Nonnegative Matrices in the Mathematical Sciences
[4]   A relaxed generalized Newton iteration method for generalized absolute value equations [J].
Cao, Yang ;
Shi, Quan ;
Zhu, Sen-Lai .
AIMS MATHEMATICS, 2021, 6 (02) :1258-1275
[5]  
Chen CR, 2021, Arxiv, DOI arXiv:2001.05781
[6]   Exact and inexact Douglas-Rachford splitting methods for solving large-scale sparse absolute value equations [J].
Chen, Cairong ;
Yu, Dongmei ;
Han, Deren .
IMA JOURNAL OF NUMERICAL ANALYSIS, 2023, 43 (02) :1036-1060
[7]   An inverse-free dynamical system for solving the absolute value equations [J].
Chen, Cairong ;
Yang, Yinong ;
Yu, Dongmei ;
Han, Deren .
APPLIED NUMERICAL MATHEMATICS, 2021, 168 :170-181
[8]  
Cottle RW., 1992, The linear complementarity problem
[9]   A new SOR-like method for solving absolute value equations [J].
Dong, Xu ;
Shao, Xin-Hui ;
Shen, Hai-Long .
APPLIED NUMERICAL MATHEMATICS, 2020, 156 :410-421
[10]   A generalization of the Gauss-Seidel iteration method for solving absolute value equations [J].
Edalatpour, Vahid ;
Hezari, Davod ;
Salkuyeh, Davod Khojasteh .
APPLIED MATHEMATICS AND COMPUTATION, 2017, 293 :156-167
123456