Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 709-726.
Published online: 2019-04
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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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0151}, url = {http://global-sci.org/intro/article_detail/nmtma/13127.html} }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.