Volume 9, Issue 1
A Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems

East Asian J. Appl. Math., 9 (2019), pp. 102-121.

Published online: 2019-01

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• Abstract

A general RTMS iteration method for linear complementarity problems is proposed. Choosing various pairs of relaxation parameters, we obtain new two-sweep modulus-based matrix splitting iteration methods and already known iteration procedures such as the MS [1] and TMS [27] iteration methods. If the system matrix is positive definite or an $H$+-matrix and the relaxation parameters $ω$1 and $ω$satisfy the inequality 0 ≤ $ω$1,$ω$2 ≤ 1, sufficient conditions for the uniform convergence of MS, TMS and NTMS iteration methods are established. Numerical results show that with quasi-optimal parameters, RTMS iteration method outperforms MS and TMS iteration methods in terms of computing efficiency

• Keywords

Linear complementarity problem matrix splitting iteration method relaxation convergence.

65F10 65F35 65H10

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@Article{EAJAM-9-102, author = {}, title = {A Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {1}, pages = {102--121}, abstract = {

A general RTMS iteration method for linear complementarity problems is proposed. Choosing various pairs of relaxation parameters, we obtain new two-sweep modulus-based matrix splitting iteration methods and already known iteration procedures such as the MS [1] and TMS [27] iteration methods. If the system matrix is positive definite or an $H$+-matrix and the relaxation parameters $ω$1 and $ω$satisfy the inequality 0 ≤ $ω$1,$ω$2 ≤ 1, sufficient conditions for the uniform convergence of MS, TMS and NTMS iteration methods are established. Numerical results show that with quasi-optimal parameters, RTMS iteration method outperforms MS and TMS iteration methods in terms of computing efficiency

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.020318.220618}, url = {http://global-sci.org/intro/article_detail/eajam/12937.html} }
TY - JOUR T1 - A Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems JO - East Asian Journal on Applied Mathematics VL - 1 SP - 102 EP - 121 PY - 2019 DA - 2019/01 SN - 9 DO - http://dor.org/10.4208/eajam.020318.220618 UR - https://global-sci.org/intro/article_detail/eajam/12937.html KW - Linear complementarity problem KW - matrix splitting KW - iteration method KW - relaxation KW - convergence. AB -

A general RTMS iteration method for linear complementarity problems is proposed. Choosing various pairs of relaxation parameters, we obtain new two-sweep modulus-based matrix splitting iteration methods and already known iteration procedures such as the MS [1] and TMS [27] iteration methods. If the system matrix is positive definite or an $H$+-matrix and the relaxation parameters $ω$1 and $ω$satisfy the inequality 0 ≤ $ω$1,$ω$2 ≤ 1, sufficient conditions for the uniform convergence of MS, TMS and NTMS iteration methods are established. Numerical results show that with quasi-optimal parameters, RTMS iteration method outperforms MS and TMS iteration methods in terms of computing efficiency

Xiaofei Peng, Meng Wang & Wen Li. (2020). A Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems. East Asian Journal on Applied Mathematics. 9 (1). 102-121. doi:10.4208/eajam.020318.220618
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