In this paper, by seeking the zero and the positive entry positions of the solution, we provide a direct method, called the reduced order method, for solving the linear complementarity problem with an M-matrix. By this method, the linear complementarity problem is transformed into a low order linear complementarity problem with some low order linear equations and the solution is constructed by the solution of the low order linear complementarity problem and the solutions of these low order linear equations in the transformations. In order to show the accuracy and the effectiveness of the method, the corresponding numerical experiments are performed.
Fang, XM., Zhao, HJ., Li, J. et al. The Reduced Order Method for Solving the Linear Complementarity Problem with an M-Matrix. J Nonlinear Math Phys (2022). https://doi.org/10.1007/s44198-022-00029-w
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Journal of Nonlinear Mathematical Physics