A relaxation two-sweep modulus-based matrix splitting iteration method for horizontal linear complementarity problems

By utilizing the relaxation and two-sweep techniques to the modulus-based matrix splitting (MMS) method, we construct a relaxation two-sweep modulus-based matrix splitting (RTMMS) iteration method for solving the horizontal linear complementarity problems (HLCP) in this work. The proposed RTMMS iteration method includes the MMS one and generalizes the RTMMS one for the linear complementarity problem (LCP). In addition, we establish the convergence theories of the RTMMS method and its relaxed variant with the system matrices being H+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{+}$$\end{document}-matrices. Numerical experiments validate that the RTMMS iteration method is efficient, and it can achieve higher computing efficiency compared with the MMS, accelerated MMS (AMMS) and two-step MMS (TMMS) ones.