A general modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems

By introducing a new positive diagonal parameter matrix, a general modulus-based matrix splitting iteration method and a general two-steps modulus-based matrix splitting iteration method for solving nonlinear complementarity problem of H-matrices are proposed. The two methods can reduce to the existing modulus-based matrix splitting iteration method by choosing special positive diagonal parameter matrices and splitting. Hence they generalize the existing modulus-based matrix splitting iteration method for solving linear and nonlinear complementarity problems. The convergence analysis of the two methods are given by the properties of H-matrix. The H-splitting assumption in the sufficient condition of convergence is weaker than the H-compatible splitting assumption of the existing modulus-based matrix splitting iteration method for nonlinear complementarity problem; In the other hand, the convergence domain of the positive diagonal parameter matrix is larger than that in the existing modulus-based matrix splitting iteration method for nonlinear complementarity problem. So the convergence results of the methods improve the existing ones, which shows the significance of introducing the new positive diagonal parameter matrix.