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

doi:10.1007/s42967-023-00311-8

Abstract

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

Key words: Horizontal quasi-complementarity problem (HQCP), Modulus-based method, Matrix splitting, Convergence

CLC Number:

65F10
65F50

Lu-Xin Wang, Qin-Qin Shen, Yang Cao. Modulus-Based Matrix Splitting Iteration Method for Horizontal Quasi-complementarity Problem[J]. Communications on Applied Mathematics and Computation, 2025, 7(4): 1308-1332.

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URL: https://www.camc.shu.edu.cn/EN/10.1007/s42967-023-00311-8

https://www.camc.shu.edu.cn/EN/Y2025/V7/I4/1308

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