The solution of the absolute value equations using two generalized accelerated overrelaxation methods

被引：10
作者：
Ali, Rashid [1 ]
Pan, Kejia [1 ]
机构：
[1] Cent South Univ, Sch Math & Stat, HNP LAMA, Changsha 410083, Hunan, Peoples R China
来源：
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2022年 / 15卷 / 08期
关键词：
Absolute value equations; generalized accelerated overrelaxation; matrix splitting; convergence; numerical experiments; SPLITTING ITERATION METHODS; LINEAR COMPLEMENTARITY;
D O I：
10.1142/S1793557122501546
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Finding the solution of the absolute value equations (AVEs) has attracted much attention in recent years. In this paper, we propose and analyze two generalized accelerated overrelaxation (AOR) methods for solving AVEs Ax -|x| = b, where A is an element of R-nxn is an M-matrix. Furthermore, we discuss the convergence of the methods under some suitable assumptions. Numerical results are given to verify the effectiveness of our methods.
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页数：13
相关论文
共 32 条
[1]   Solving absolute value equation using complementarity and smoothing functions [J].
Abdallah, L. ;
Haddou, M. ;
Migot, T. .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 327 :196-207
[2]   A polynomial-time weighted path-following interior-point algorithm for linear optimization [J].
Achache, Mohamed .
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2020, 13 (02)
[3]  
Ali R., 2020, Math Theory Appl, V40, P44
[4]  
[Anonymous], 1962, Iterative analysis
[5]   Modulus-based matrix splitting iteration methods for linear complementarity problems [J].
Bai, Zhong-Zhi .
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2010, 17 (06) :917-933
[6]   A globally and quadratically convergent method for absolute value equations [J].
Caccetta, Louis ;
Qu, Biao ;
Zhou, Guanglu .
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2011, 48 (01) :45-58
[7]  
Chen CR, 2021, Arxiv, DOI arXiv:2001.05781
[8]  
Cottle R.W., 1992, The Linear Complementarity Problem
[9]   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
[10]   TWO CSCS-BASED ITERATION METHODS FOR SOLVING ABSOLUTE VALUE EQUATIONS [J].
Gu, Xian-Ming ;
Huang, Ting-Zhu ;
Li, Hou-Biao ;
Wang, Sheng-Feng ;
Li, Liang .
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2017, 7 (04) :1336-1356
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