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

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 = {}, 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 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 & Junfeng Yin. (2020). 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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