The convergence of modulus-based matrix splitting iteration methods for implicit complementarity problems

Abstract

In this paper, we discuss the convergence of the modulus-based matrix splitting iteration methods for solving implicit complementarity problems. We simplify the iteration form of the modulus-based matrix splitting (MMS) iteration method, then propose the convergence conditions for both the simplified MMS iteration method and the modified MMS iteration method in terms of spectral radius and matrix norm. Besides, we provide the concrete convergence domains of the parameter matrix for the special case of the two methods. The corresponding numerical experiments are illustrated to show the presented results.