Volume 7, Issue 1
SOR-like Methods with Optimization Model for Augmented Linear Systems

Rui-Ping Wen, Su-Dan Li & Guo-Yan Meng

East Asian J. Appl. Math., 7 (2017), pp. 101-115.

Published online: 2018-02

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  • Abstract

There has been a lot of study on the SOR-like methods for solving the augmented system of linear equations since the outstanding work of Golub, Wu and Yuan (BIT 41(2001)71-85) was presented fifteen years ago. Based on the SOR-like methods, we establish a class of accelerated SOR-like methods for large sparse augmented linear systems by making use of optimization technique, which will find the optimal relaxation parameter ω by optimization models. We demonstrate the convergence theory of the new methods under suitable restrictions. The numerical examples show these methods are effective.

  • Keywords

SOR-like method, optimization, augmented linear systems, convergence.

  • AMS Subject Headings

65F10, 65F50, 15A06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-101, author = {}, title = {SOR-like Methods with Optimization Model for Augmented Linear Systems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {1}, pages = {101--115}, abstract = {

There has been a lot of study on the SOR-like methods for solving the augmented system of linear equations since the outstanding work of Golub, Wu and Yuan (BIT 41(2001)71-85) was presented fifteen years ago. Based on the SOR-like methods, we establish a class of accelerated SOR-like methods for large sparse augmented linear systems by making use of optimization technique, which will find the optimal relaxation parameter ω by optimization models. We demonstrate the convergence theory of the new methods under suitable restrictions. The numerical examples show these methods are effective.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.010916.261116a}, url = {http://global-sci.org/intro/article_detail/eajam/10737.html} }
TY - JOUR T1 - SOR-like Methods with Optimization Model for Augmented Linear Systems JO - East Asian Journal on Applied Mathematics VL - 1 SP - 101 EP - 115 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.010916.261116a UR - https://global-sci.org/intro/article_detail/eajam/10737.html KW - SOR-like method, optimization, augmented linear systems, convergence. AB -

There has been a lot of study on the SOR-like methods for solving the augmented system of linear equations since the outstanding work of Golub, Wu and Yuan (BIT 41(2001)71-85) was presented fifteen years ago. Based on the SOR-like methods, we establish a class of accelerated SOR-like methods for large sparse augmented linear systems by making use of optimization technique, which will find the optimal relaxation parameter ω by optimization models. We demonstrate the convergence theory of the new methods under suitable restrictions. The numerical examples show these methods are effective.

Rui-Ping Wen, Su-Dan Li & Guo-Yan Meng. (2020). SOR-like Methods with Optimization Model for Augmented Linear Systems. East Asian Journal on Applied Mathematics. 7 (1). 101-115. doi:10.4208/eajam.010916.261116a
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