GLOBAL RELAXED MODULUS-BASED SYNCHRONOUS BLOCK MULTISPLITTING MULTI-PARAMETERS METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

Litao Zhang; Xianyu Zuo

doi:10.11948/20190177

2020 Volume 10 Issue 4

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Litao Zhang, Xianyu Zuo. GLOBAL RELAXED MODULUS-BASED SYNCHRONOUS BLOCK MULTISPLITTING MULTI-PARAMETERS METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1267-1281. doi: 10.11948/20190177

Citation:

Litao Zhang, Xianyu Zuo. GLOBAL RELAXED MODULUS-BASED SYNCHRONOUS BLOCK MULTISPLITTING MULTI-PARAMETERS METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1267-1281. doi: 10.11948/20190177

GLOBAL RELAXED MODULUS-BASED SYNCHRONOUS BLOCK MULTISPLITTING MULTI-PARAMETERS METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

Litao Zhang^1,,
Xianyu Zuo^4, ,

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.
Institute of Data and Knowledge Engineering, School of Computer and Information Engineering, Henan University, Kaifeng, Henan, 475004, China

Author Bio: Email address: yifanzhang2019@126.com(Y. Zhang)
Corresponding author: Email address: xianyu_zuo@163.com(X. Zuo)

Abstract

Abstract

Recently, Bai and Zhang [Numerical Linear Algebra with Applications, 2013, 20, 425Ƀ439] constructed modulus-based synchronous multisplitting methods by an equivalent reformulation of the linear complementarity problem into a system of fixed-point equations and studied the convergence of them; Li et al. [Journal of Nanchang University (Natural Science), 2013, 37, 307Ƀ312] studied synchronous block multisplitting iteration methods; Zhang and Li [Computers and Mathematics with Application, 2014, 67, 1954Ƀ1959] analyzed and obtained the weaker convergence results for linear complementarity problems. In this paper, we generalize their algorithms and further study global relaxed modulus-based synchronous block multisplitting multi-parameters methods for linear complementarity problems. Furthermore, we give the weaker convergence results of our new method in this paper when the system matrix is a block $ H_{+}- $matrix. Therefore, new results provide a guarantee for the optimal relaxation parameters, please refer to [A. Hadjidimos, M. Lapidakis and M. Tzoumas, SIAM Journal on Matrix Analysis and Applications, 2012, 33, 97Ƀ110, (dx.doi.org/10.1137/100811222)], where optimal parameters are determined.
- Global relaxed modulus-based method /
- linear complementarity problem /
- block multisplitting, block H₊-matrix /
- synchronous multisplitting

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References

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