RELAXED MODULUS-BASED SYNCHRONOUS MULTISPLITTING MULTI-PARAMETERS TOR (TWO-PARAMETERS OVER-RELAXATION) METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

Li-Tao Zhang; Ying-Chao Zhao; Yi-Fan Zhang; Sheng-Kun Li

doi:10.11948/20210166

2022 Volume 12 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2022 > 12(4): 1403-1417

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Li-Tao Zhang, Ying-Chao Zhao, Yi-Fan Zhang, Sheng-Kun Li. RELAXED MODULUS-BASED SYNCHRONOUS MULTISPLITTING MULTI-PARAMETERS TOR (TWO-PARAMETERS OVER-RELAXATION) METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1403-1417. doi: 10.11948/20210166

Citation:

Li-Tao Zhang, Ying-Chao Zhao, Yi-Fan Zhang, Sheng-Kun Li. RELAXED MODULUS-BASED SYNCHRONOUS MULTISPLITTING MULTI-PARAMETERS TOR (TWO-PARAMETERS OVER-RELAXATION) METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1403-1417. doi: 10.11948/20210166

RELAXED MODULUS-BASED SYNCHRONOUS MULTISPLITTING MULTI-PARAMETERS TOR (TWO-PARAMETERS OVER-RELAXATION) METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

1.
School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou, Henan, 450015, China
2.
College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, 453007, China
3.
Henan province Synergy Innovation Center of Aviation economic development, Zhengzhou, Henan, 450015, China
4.
Department of Sport and Public Art, Zhengzhou University of Aeronautics, Zhengzhou, Henan, 450015, China
5.
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan, 610225, China

Corresponding author: Email: litaozhang@163.com(L. Zhang)

Abstract

Abstract

In 2013, Bai and Zhang [Numerical Linear Algebra with Applications, 20(2013), 425–439] constructed modulus-based synchronous multisplitting methods by an equivalent reformulation of the linear complementarity problems into a system of fixed-point equations and studied the convergence of them. In 2014, Zhang and Li [Computers and Mathematics with Application, 67(2014), 1954–1959] analyzed and obtained the weaker convergence results for linear complementarity problems. In 2008, Zhang et.al. [International Journal of Computer Mathematics, 85(2), 2008, 211–224] presented global relaxed non-stationary multisplitting multi-parameter method by introducing some relaxed parameters. In this paper, we generalize Bai and Zhang's methods and study relaxed modulus-based synchronous multisplitting multi-parameters TOR (two-parameters over-relaxation, abbreviated as TOR) methods for linear complementarity problems. Furthermore, the convergence results of our new method in this paper are given when the system matrix is an $ H_{+}- $matrix.
- Modulus-based method /
- linear complementarity /
- successive relaxation /
- H₊-matrix
MSC: 65F10, 65F50, 90C33, 65G40

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References

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