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Volume 11, Issue 1
On the Convergence of Two-Step Modulus-Based Matrix Splitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems with $H_+$-Matrices

Rui Li, Yan Wang & Junfeng Yin

DOI: 10.4208/nmtma.OA-2017-0004

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 128-139.

Published online: 2018-11

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  • Abstract

We propose the two-step modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems. The corresponding convergence theory is established when the system matrix is an $H_+$-matrix. Theoretical analysis gives the choice of parameter matrix involved based on the $H$-compatible splitting of the system matrix. Moreover, in actual implementation, the choices of iterative parameters for two-step modulus-based accelerated overrelaxation methods are studied. Numerical experiments show that the method is efficient and further verify the convergence theorems.

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@Article{NMTMA-11-128, author = {Rui Li, Yan Wang and Junfeng Yin}, title = {On the Convergence of Two-Step Modulus-Based Matrix Splitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems with $H_+$-Matrices}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {1}, pages = {128--139}, abstract = {

We propose the two-step modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems. The corresponding convergence theory is established when the system matrix is an $H_+$-matrix. Theoretical analysis gives the choice of parameter matrix involved based on the $H$-compatible splitting of the system matrix. Moreover, in actual implementation, the choices of iterative parameters for two-step modulus-based accelerated overrelaxation methods are studied. Numerical experiments show that the method is efficient and further verify the convergence theorems.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0004}, url = {http://global-sci.org/intro/article_detail/nmtma/10646.html} }
TY - JOUR T1 - On the Convergence of Two-Step Modulus-Based Matrix Splitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems with $H_+$-Matrices AU - Rui Li, Yan Wang & Junfeng Yin JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 128 EP - 139 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.OA-2017-0004 UR - https://global-sci.org/intro/article_detail/nmtma/10646.html KW - AB -

We propose the two-step modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems. The corresponding convergence theory is established when the system matrix is an $H_+$-matrix. Theoretical analysis gives the choice of parameter matrix involved based on the $H$-compatible splitting of the system matrix. Moreover, in actual implementation, the choices of iterative parameters for two-step modulus-based accelerated overrelaxation methods are studied. Numerical experiments show that the method is efficient and further verify the convergence theorems.

Rui Li, Yan Wang and Junfeng Yin. (2018). On the Convergence of Two-Step Modulus-Based Matrix Splitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems with $H_+$-Matrices. Numerical Mathematics: Theory, Methods and Applications. 11 (1). 128-139. doi:10.4208/nmtma.OA-2017-0004
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