A Two-Step Modulus-Based Matrix Splitting Iteration Method Without Auxiliary Variables for Solving Vertical Linear Complementarity Problems

doi:10.1007/s42967-023-00280-y

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (4): 2475-2492.doi: 10.1007/s42967-023-00280-y

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A Two-Step Modulus-Based Matrix Splitting Iteration Method Without Auxiliary Variables for Solving Vertical Linear Complementarity Problems

Hua Zheng¹, Xiaoping Lu², Seakweng Vong³

1 School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, Guangdong, China;
2 School of Computer Science and Engineering, Macau University of Science and Technology, Macau, China;
3 Department of Mathematics, University of Macau, Macau, China

Received:2023-01-08 Revised:2023-03-20 Accepted:2023-04-21 Published:2024-12-20
Contact: Seakweng Vong,E-mail:swvong@um.edu.mo;Hua Zheng,E-mail:hzheng@sgu.edu.cn;Xiaoping Lu,E-mail:xplu@must.edu.mo E-mail:swvong@um.edu.mo;hzheng@sgu.edu.cn;xplu@must.edu.mo

Abstract

Abstract: In this paper, a two-step iteration method is established which can be viewed as a generalization of the existing modulus-based methods for vertical linear complementarity problems given by He and Vong (Appl. Math. Lett. 134:108344, 2022). The convergence analysis of the proposed method is established, which can improve the existing results. Numerical examples show that the proposed method is efficient with the two-step technique.

Key words: Vertical linear complementarity problem, Modulus-based matrix splitting, Two-step metho

Hua Zheng, Xiaoping Lu, Seakweng Vong. A Two-Step Modulus-Based Matrix Splitting Iteration Method Without Auxiliary Variables for Solving Vertical Linear Complementarity Problems[J]. Communications on Applied Mathematics and Computation, 2024, 6(4): 2475-2492.

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A Two-Step Modulus-Based Matrix Splitting Iteration Method Without Auxiliary Variables for Solving Vertical Linear Complementarity Problems

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