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

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

DOI: 10.4208/nmtma.OA-2017-0151

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

Published online: 2019-04

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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.

  • Keywords

Nonlinear complementarity problem, modulus-based synchronous multisplitting, iteration method, $H_+$-matrix, $H$-compatible splitting, convergence.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-12-709, author = {Yu-Jiang Wu, Gui-Lin Yan and Ai-Li Yang}, title = {Modulus-Based Synchronous Multisplitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {12}, number = {3}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0151}, url = {http://global-sci.org/intro/article_detail/nmtma/13127.html} }
TY - JOUR T1 - Modulus-Based Synchronous Multisplitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems AU - Yu-Jiang Wu, Gui-Lin Yan & Ai-Li Yang 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 -

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.

Yu-Jiang Wu, Gui-Lin Yan and Ai-Li Yang. (2019). Modulus-Based Synchronous Multisplitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems. Numerical Mathematics: Theory, Methods and Applications. 12 (3). 709-726. doi:10.4208/nmtma.OA-2017-0151
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