Modulus-Based Multisplitting Iteration Methods for a Class of Nonlinear Complementarity Problems

Abstract

Modulus-based multisplitting iterative methods for large sparse nonlinear complementarity problems are developed. The approach is based on a reformulation of nonlinear complimentarily problems as implicit fixed-point equations and includes Jacobi, Gauss-Seidel and SOR iteration methods. For systems with positive definite matrices the convergence of the methods is proved. The methods are suitable for implementation on multiprocessor systems and numerical experiments confirm their high efficiency.