收稿日期: 2021-04-08
网络出版日期: 2023-01-31
基金资助
国家自然科学基金资助项目(12171307);山东高校科技计划资助项目(J16LI04);青岛农业大学高层次人才资助项目(1120068)
Accelerated two-step modulus-based matrix splitting iteration method to solve the nonlinear complementarity problem
Received date: 2021-04-08
Online published: 2023-01-31
程冰, 王广彬, 谭福平 . 求解非线性互补问题的一类加速的两步模基矩阵分裂迭代法[J]. 上海大学学报(自然科学版), 2022 , 28(6) : 1106 -1112 . DOI: 10.12066/j.issn.1007-2861.2346
In this paper, we construct an accelerated two-step modulus-based matrix splitting iteration method based on multiple splittings of the system matrix for the nonlinear complementarity problem. And we prove its convergence when the system matrix is an H-matrix with positive diagonal elements. Numerical experiments show that the proposed method is efficient.
| [1] | Bai Z Z. Modulus-based matrix splitting iteration methods for linear complementarity problems[J]. Numer Linear Algebra Appl, 2010, 17(6): 917-933. |
| [2] | Ke Y F, Ma C F, Zhang H. The modulus-based matrix splitting iteration methods for second-order cone linear complementarity problems[J]. Numer Algor, 2018, 79(4): 1283-1303. |
| [3] | Xia Z C, Li C L. Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problem[J]. Appl Math Comput, 2015, 271(1): 34-42. |
| [4] | Huang B H, Ma C F. Accelerated modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems[J]. Comp Appl Math, 2018, 37(3): 3053-3076. |
| [5] | Li R, Yin J F. Accelerated modulus-based matrix splitting iteration methods for a restricted class of nonlinear complementarity problems[J]. Numer Algor, 2017, 75(2): 339-358. |
| [6] | Ke Y F, Ma C F, Zhang H. The relaxation modulus-based matrix splitting iteration methods for circular cone nonlinear complementarity problems[J]. Comp Appl Math, 2018, 37(5): 6795-6820. |
| [7] | Li R, Wang Y, Yin J F. On the convergence of two-step modulus-based matrix splitting iteration methods for a restricted class of nonlinear complementarity problems with $H_{+}$-matrices[J]. Numer Math Theor Meth Appl, 2018, 11(1): 128-139. |
| [8] | Berman A, Plemmons R J. Nonnegative matrices in the mathematical sciences[M]. New York: Academic Press, 1979. |
| [9] | Li W, Zheng H. A preconditioned modulus-based iteration method for solving linear complementarity problems of $H_{+}$-matrices[J]. Linear and Multilinear Algebra, 2016, 64(7): 1-14. |
| [10] | Hu J G. Estimates of $\|B^{-1}A\|_{\infty}$ and their applications[J]. Math Num Sin, 1982, 4(3): 272-282. |
| [11] | Xu W W, Liu H. A modified general modulus-based matrix splitting method for linear complementarity problems of $H$-matrices[J]. Linear Algebra Appl, 2014, 458(10): 626-637. |
/
| 〈 |
|
〉 |
