Relaxed Modulus-Based Matrix Splitting Methods for the Linear Complementarity Problem

In this paper, we obtain a new equivalent fixed-point form of the linear complementarity problem by introducing a relaxed matrix and establish a class of relaxed modulus-based matrix splitting iteration methods for solving the linear complementarity problem. Some sufficient conditions for guaranteeing the convergence of relaxed modulus-based matrix splitting iteration methods are presented. Numerical examples are offered to show the efficacy of the proposed methods.

Automated summary

In this paper, a new equivalent fixed-point form of the linear complementarity problem is obtained by introducing a relaxed matrix, and a class of relaxed modulus-based matrix splitting iteration methods is established to solve the problem. Sufficient conditions for ensuring the convergence of relaxed modulus-based matrix splitting iteration methods are provided, and numerical examples are used to demonstrate the effectiveness of the proposed methods.