Modulus-based inexact non-alternating preconditioned splitting method for linear complementarity problems

For the large sparse linear complementarity problem, by reformulating it as implicit fixed-point equations, we establish a modulus-based iteration method with the aid of an inexact non-alternating preconditioned matrix splitting iteration method used as an inner iteration to solve the module equations rapidly in each iteration step. The convergence properties of this method are carefully demonstrated under certain conditions. Numerical results, including the numbers of iteration steps and the computing times, validate that our method is superior to the other three iteration methods.