The simplified modulus-based matrix splitting iteration method for the nonlinear complementarity problem

被引：1
作者：
Fang, Ximing [1 ]
机构：
[1] Zhaoqing Univ, Sch Math & Stat, Zhaoqing 526000, Peoples R China
来源：
AIMS MATHEMATICS | 2024年 / 9卷 / 04期
关键词：
nonlinear complementarity; numerical solution; iteration method; matrix spitting; convergence;
D O I：
10.3934/math.2024416
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the simplified modulus-based matrix splitting iteration method was extended to solve the nonlinear complementarity problem, and the convergence conditions were presented from the spectral radius and the matrix norm. Then, for the special cases of this method, we provided some concrete convergence conditions as well as the quasi-optimal parameter matrix. Moreover, some numerical examples were illustrated to show the validity of the convergence results.
引用
收藏
页码：8594 / 8609
页数：16
相关论文
共 30 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]  
Berman A., 1994, Nonnegative Matrices in the Mathematical Sciences, DOI [10.1137/1023089, DOI 10.1137/1023089]
[3]   An interior proximal point algorithm for nonlinear complementarity problems [J].
Bnouhachem, Abdellah ;
Noor, Muhammad Aslam .
NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2010, 4 (03) :371-380
[4]   COMPARISONS OF REGULAR SPLITTINGS OF MATRICES [J].
CSORDAS, G ;
VARGA, RS .
NUMERISCHE MATHEMATIK, 1984, 44 (01) :23-35
[5]   On the choice of parameters in MAOR type splitting methods for the linear complementarity problem [J].
Cvetkovic, Lj. ;
Hadjidimos, A. ;
Kostic, V. .
NUMERICAL ALGORITHMS, 2014, 67 (04) :793-806
[6]   The convergence of a modulus-based matrix splitting iteration method for solving the implicit complementarity problems [J].
Fang, Ximing .
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2023, 69 (01) :853-870
[7]   Convergence of modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems [J].
Fang, Ximing .
NUMERICAL ALGORITHMS, 2022, 90 (03) :931-950
[8]   New convergence results of the modulus-based methods for vertical linear complementarity problems [J].
Guo, Wen-Xiu ;
Zheng, Hua ;
Peng, Xiao-Fei .
APPLIED MATHEMATICS LETTERS, 2023, 135
[9]   ON ITERATIVE SOLUTION FOR LINEAR COMPLEMENTARITY PROBLEM WITH AN H+-MATRIX [J].
Hadjidimos, A. ;
Lapidakis, M. ;
Tzoumas, M. .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2012, 33 (01) :97-110
[10]   Modulus-based matrix splitting iteration methods for a class of implicit complementarity problems [J].
Hong, Jun-Tao ;
Li, Chen-Liang .
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2016, 23 (04) :629-641
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