Abstract
In this paper, for solving the vertical linear complementarity problem (VLCP) effectively, a two-step new modulus-based matrix splitting (TNMMS) iteration method is introduced. Its convergence properties are discussed in depth. The efficiency of the proposed method is confirmed by some numerical experiments from the 2-D boundary problem. Numerical results show that the proposed method is superior to some existing methods, such as the two modulus-based matrix splitting (TMMS) iteration method (Numer. Algor., 2011, 57: 83–99) and the new modulus-based matrix splitting (NMMS) iteration method (Optim., 2023, 72: 2499–2516).
Acknowledgments
The authors would like to thank associate editor and two anonymous referees for providing helpful suggestions, which greatly improved the paper.
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No potential conflict of interest was reported by the author(s).
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Notes on contributors
Cuixia Li
Cuixia Li, work at Yunnan Normal University. Prof. Li is interested in numerical linear algebra, including complementarity problem, absolute value equation and so on.
Shiliang Wu
Shiliang Wu, work at Yunnan Normal University. Prof. Wu at present focus on numerical linear algebra and optimization.