Modulus-Based Multisplitting Iteration Method for a Class of Weakly Nonlinear Complementarity Problem

doi:10.1007/s42967-020-00074-6

Communications on Applied Mathematics and Computation ›› 2021, Vol. 3 ›› Issue (3): 419-428.doi: 10.1007/s42967-020-00074-6

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Modulus-Based Multisplitting Iteration Method for a Class of Weakly Nonlinear Complementarity Problem

Guangbin Wang¹, Fuping Tan²

1 Department of Mathematics, Qingdao Agricultural University, Qingdao 266109, Shandong Province, China;
2 Department of Mathematics, Shanghai University, Shanghai 200444, China

收稿日期:2019-08-02 修回日期:2020-04-18 出版日期:2021-09-20 发布日期:2021-09-16
通讯作者: Guangbin Wang, Fuping Tan E-mail:fptan@shu.edu.cn;wguangbin750828@sina.com
基金资助:
The authors are grateful to the referees for valuable comments. This work was supported by the National Natural Science Foundation of China (Grant No. 11771275) and the Science and Technology Program of Shandong Universities (No. J16LI04).

Modulus-Based Multisplitting Iteration Method for a Class of Weakly Nonlinear Complementarity Problem

Guangbin Wang¹, Fuping Tan²

1 Department of Mathematics, Qingdao Agricultural University, Qingdao 266109, Shandong Province, China;
2 Department of Mathematics, Shanghai University, Shanghai 200444, China

Received:2019-08-02 Revised:2020-04-18 Online:2021-09-20 Published:2021-09-16
Contact: Guangbin Wang, Fuping Tan E-mail:fptan@shu.edu.cn;wguangbin750828@sina.com
Supported by:
The authors are grateful to the referees for valuable comments. This work was supported by the National Natural Science Foundation of China (Grant No. 11771275) and the Science and Technology Program of Shandong Universities (No. J16LI04).

摘要/Abstract

摘要： In this paper, we present a modulus-based multisplitting iteration method based on multisplitting of the system matrix for a class of weakly nonlinear complementarity problem. And we prove the convergence of the method when the system matrix is an H₊-matrix. Finally, we give two numerical examples.

关键词: Modulus-based multisplitting method, Nonlinear complementarity problem, H-matrix

Abstract: In this paper, we present a modulus-based multisplitting iteration method based on multisplitting of the system matrix for a class of weakly nonlinear complementarity problem. And we prove the convergence of the method when the system matrix is an H₊-matrix. Finally, we give two numerical examples.

Key words: Modulus-based multisplitting method, Nonlinear complementarity problem, H-matrix

中图分类号:

65F10
15B99

Guangbin Wang, Fuping Tan. Modulus-Based Multisplitting Iteration Method for a Class of Weakly Nonlinear Complementarity Problem[J]. Communications on Applied Mathematics and Computation, 2021, 3(3): 419-428.

参考文献

1. Bai, Z.-Z.:On the convergence of the multisplitting methods for linear complementarity problem. SIAM J. Matrix Anal. Appl. 21, 67-78 (1999)
2. Bai, Z.-Z.:Modulus-based matrix splitting iteration methods for linear complementarity problems. Numer. Linear Algebra Appl. 17, 917-933 (2010)
3. Berman, A., Plemmons, R.J.:Nonnegative Matrices in the Mathematical Sciences. SIAM, Philadelphia (1994)
4. Dong, J.-L., Jiang, M.-Q.:A modified modulus method for symmetric positive-definite linear complementarity problems. Numer. Linear Algebra Appl. 16, 129-143 (2009)
5. Hadjidimos, A., Zhang, L.-L.:Comparison of three classes of algorithms for the solution of the linear complementarity problem with an H₊-matrix. J. Comput. Appl. Math. 336, 175-191 (2018)
6. Huang, B.-H., Ma, C.-F.:Accelerated modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems. Comp. Appl. Math. 37, 3053-3076 (2018)
7. Li, W.:A general modulus-based matrix splitting method for linear complementarity problems of H -matrices. Appl. Math. Lett. 26, 1159-1164 (2013)
8. Li, R., Yin, J.-F.:Accelerated modulus-based matrix splitting iteration methods for a restricted class of nonlinear complementarity problems. Numer. Algor. 75, 339-358 (2017)
9. Li, W., Zheng, H.:A preconditioned modulus-based iteration method for solving linear complementarity problems of H-matrices. Linear Multilinear Algebra 64, 1390-1403 (2016)
10. Luo, M.-J., Wang, Y.-Y., Liu, H.-L.:Convergence results of a matrix splitting algorithm for solving weakly nonlinear complementarity problems. J. Inequal. Appl. 203, 1-9 (2016)
11. Van Bokhoven, W.M.G.:Piecewise-Linear Modelling and Analysis. Proefschrift, Eindhoven (1981)
12. Varga, R.S.:Matrix Iterative Analysis. Springer, Berlin (2000)
13. Wu, Y.-J., Yan, G.-L., Yang, A.-L.:Modulus-based synchronous multisplitting iteration methods for a restricted class of nonlinear complementarity problems. Numer. Math. Theory Methods Appl. 12, 709-726 (2019)
14. Xia, Z.-C., Li, C.-L.:Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problem. Appl. Math. Comput. 271, 34-42 (2015)
15. Xu, W.-W., Liu, H.:A modified general modulus-based matrix splitting method for linear comple mentarity problems of H-matrices. Linear Algebra Appl. 458, 626-637 (2014)
16. Xu, H.-R., Chen, R.-L., Xie, S.-L., Wu, L.:Modulus-based multisplitting iteration methods for a class of nonlinear complementarity problems. E. Asian J. Appl. Math. 8, 519-530 (2018)
17. Zheng, N., Yin, J.-F.:Convergence of accelerated modulus-based matrix splitting iteration methods for linear complementarity problem with an H₊-matrix. J. Comput. Appl. Math. 260, 281-293 (2014)

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Modulus-Based Multisplitting Iteration Method for a Class of Weakly Nonlinear Complementarity Problem

Modulus-Based Multisplitting Iteration Method for a Class of Weakly Nonlinear Complementarity Problem

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