Modulus-based Synchronous Multisplitting Iteration Methods For A Restricted Class Of Nonlinear Complementarity Problems

Complementary problem is defined as to find a pair of nonnegative variables in a certain space to make it meet a complementary relationship,and the relationship reflects a basic relations of the widespread.Since 60s of the last century,the complementary problem was introduced and researched,it has received extensive attention of numerous mathematical researchers and enthusiasts.Complementary problems are not only a hot topic in the field of mathematics,but their algorithms are also constantly updated.They have close connection with game theory,programming,economics,mechanics disciplines;while there is a wide range of applications in scientific computing and engineering applications.This paper aims to consider an effective algorithm for a restricted class of non-linear complementarity problems.It is first reformulated into an equivalent implicit fixed-point equation in this work.Then we establish a modulus-based synchronous multisplitting iteration method based on the fixed-point equation.Moreover,several kinds of special choices of the iteration methods including multisplitting relaxation methods such as Jacobi,Gauss-Seidel,successive overrelaxation(SOR),and accelerated overrelaxation(AOR)of the modulus type are presented.Convergence theorems for these iteration methods are proven when the system matrix A is an H+-matrix.Numerical results are also provided to confirm the efficiency of these methods in actual implementations.