Modulus-Based Matrix Splitting Iteration Method for Horizontal Quasi-complementarity Problem

Abstract

In this paper, the modulus-based matrix splitting (MMS) iteration method is extended to solve the horizontal quasi-complementarity problem (HQCP), which is characterized by the presence of two system matrices and two nonlinear functions. Based on the specific matrix splitting of the system matrices, a series of MMS relaxation iteration methods are presented. Convergence analyses of the MMS iteration method are carefully studied when the system matrices are positive definite matrices and

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, respectively. Finally, two numerical examples are given to illustrate the efficiency of the proposed MMS iteration methods.

Keywords

Horizontal quasi-complementarity problem (HQCP) / Modulus-based method / Matrix splitting / Convergence

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Funding

National Natural Science Foundation of China(11771225)

Qinglan Project of Jiangsu Province of China

Science and Technology Project of Nantong City(JC2021198)

RIGHTS & PERMISSIONS

Shanghai University