The nonlinear lopsided PSS-like and HSS-like modulus-based matrix splitting iteration methods for horizontal linear complementarity problem

For solving horizontal linear complementarity problem (HLCP), we propose a nonlinear lopsided PSS-like modulus-based matrix splitting iteration method and a new nonlinear lopsided PSS-like modulus-based matrix splitting iteration method according to the characteristics of the HLCP. The proposed methods contain the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method and a new nonlinear lopsided HSS-like modulus-based matrix splitting iteration method. When the system matrices are positive definite matrices, we analyze the proposed methods in theory and prove the convergence of these methods. Numerical experiments in this paper demonstrate the effectiveness of the proposed methods.