On the Convergence of Two-Step Modulus-Based Matrix Splitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems with $H_+$-Matrices

Abstract

We propose the two-step modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems. The corresponding convergence theory is established when the system matrix is an $H_+$-matrix. Theoretical analysis gives the choice of parameter matrix involved based on the $H$-compatible splitting of the system matrix. Moreover, in actual implementation, the choices of iterative parameters for two-step modulus-based accelerated overrelaxation methods are studied. Numerical experiments show that the method is efficient and further verify the convergence theorems.