The modulus-based matrix double splitting iteration method for linear complementarity problems

Abstract

For large sparse linear complementarity problems, through reformulating them as implicit fixed-point equations, we propose a modulus-based matrix double splitting (MB-DS) iteration method by splitting the system matrices twice. Besides, the convergence of this method is proved when the system matrix is a P-matrix and an H+-matrix. In some special cases, we present the convergence regions and the optimal values for the parameter ω. In order to show the efficiency of the MB-DS iteration method and the effectiveness of the optimal parameter, some corresponding numerical experiments are performed.