The Monomial Preconditioned SSOR Method for Linear Complementarity Problem

Abstract

This paper aims to show that the existing preconditioned symmetric successive over-relaxation (SSOR) approach to solving the linear complementarity problem (LCP) is not valid. To overcome the flaws, we propose an efficient preconditioner called the monomial preconditioner. The convergence behavior of the proposed model is also established. Meanwhile, the efficiency of the new method is verified by numerical experiments.INDEX TERMS Linear complementarity problem, M-matrix, preconditioning, projected model, SSOR method.

A Fast Algorithm for Solving a Class of the Linear Complementarity Problem in a Finite Number of Steps

“…Newly, in [30], for solving the linear complementarity problem, Wang et al [31] propose an interior point method to find the solution of the linear complementarity problem, where the matrix is a real square hidden Z-matrix. In this context, we can see the works [31][32][33][34][35][36][37][38][39].…”

Generalized SOR-Like Iteration Method for Linear Complementarity Problem

“…Further discussing the modulus-based matrix splitting iteration method and its various versions, one can see [11][12][13][14][15][16][17] for more details. In addition, for other forms of iteration methods, one can see [18][19][20][21][22].…”

A new Approach for the Modulus-Based Matrix Splitting Algorithms

“…The solution of LCPs divided into categories: direct methods and iterative methods that much attention was paid on the iterative methods. Iterative methods for solution of LCPs also divided into projected iterative methods [4]- [9], modulus algorithms [10]- [12], modulus-based matrix splitting iterative methods [13]- [17], variant types of multisplitting iteration methods [18]- [20], and preconditioning iterative methods [21]- [23] and their references.…”