A new Approach for the Modulus-Based Matrix Splitting Algorithms

Abstract

We investigate the modulus-based matrix splitting iteration algorithms for solving the linear complementarity problems (LCPs) and propose a new model to solve it. The structure of the new model is straightforward and can be extended to other issues of type of complementarity. Convergence analysis of the new approach for the symmetric positive definite matrix is also discussed. The numerical results of the proposed approach are compared with the existing algorithms to show its efficiency. INDEX TERMS Linear complementarity problem, iterative method, matrix splitting, convergence analysis.

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

“…In [24], El foutayeni and Khaladi have shown that the linear complementarity problem LCPðM, qÞ is completely equivalent to finding the fixed point of the map x = max ð0, ðI − MÞx − qÞ, and they showed that to find an approximation of the solution to the second problem, they proposed an algorithm that starts from an arbitrary interval vector X ð0Þ , then they generalize a sequence of the interval vector ðX ðkÞ Þ k=1,⋯ that converges to the best solution of linear complementarity problems. 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].…”

“…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].…”