Modulus-Based Synchronous Multisplitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems
Year: 2019
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 709–726
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2017-0151
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 709–726
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Nonlinear complementarity problem modulus-based synchronous multisplitting iteration method $H_+$-matrix $H$-compatible splitting convergence.
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