On general fixed point method based on matrix splitting for solving linear complementarity problem

Abstract

In this article, we introduce a modified fixed point method to process the large and sparse linear complementarity problem (LCP) and formulate an equivalent fixed point equation for the LCP and show the equivalence. Also, we provide convergence conditions when the system matrix is a $P$-matrix and two sufficient convergence conditions when the system matrix is an $H_+$-matrix. To show the efficiency of our proposed method, we illustrate two numerical examples for different parameters