Volume 12, Issue 3
Modulus-Based Synchronous Multisplitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems

Yu-Jiang Wu ,  Gui-Lin Yan and Ai-Li Yang

10.4208/nmtma.OA-2017-0151

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 709-726.

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  • 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.

  • History

Published online: 2019-04

  • AMS Subject Headings

65M10, 78A48

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