TY - JOUR
T1 - Modulus-Based Synchronous Multisplitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 709
EP - 726
PY - 2019
DA - 2019/04
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2017-0151
UR - https://global-sci.org/intro/article_detail/nmtma/13127.html
KW - Nonlinear complementarity problem, modulus-based synchronous multisplitting, iteration method, $H_+$-matrix, $H$-compatible splitting, convergence.
AB - <p style="text-align: justify;">A class of nonlinear complementarity problems are first reformulated into
a series of equivalent implicit fixed-point equations in this paper. 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 extrapolated 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 coefficient matrix $A$ is an $H_+$-matrix. Numerical results are also provided to confirm the
efficiency of these methods in actual implementations.</p>