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Volume 36, Issue 4
A Modified Preconditioner for Parameterized Inexact Uzawa Method for Indefinite Saddle Point Problems

Xinhui Shao, Chen Li, Tie Zhang & Changjun Li

DOI: 10.4208/jcm.1702-m2016-0665

J. Comp. Math., 36 (2018), pp. 579-590.

Published online: 2018-06

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  • Abstract

The preconditioner for parameterized inexact Uzawa methods has been used to solve some indefinite saddle point problems. Firstly, we modify the preconditioner by making it more generalized, then we use theoretical analyses to show that the iteration method converges under certain conditions. Moreover, we discuss the optimal parameter and matrices based on these conditions. Finally, we propose two improved methods. Numerical experiments are provided to show the effectiveness of the modified preconditioner. All methods have fantastic convergence rates by choosing the optimal parameter and matrices.

  • Keywords

Preconditioner, Inexact Uzawa method, Saddle point problems, Indefiniteness, Convergence.

  • AMS Subject Headings

65F08, 65F10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xinhui1002@126.com (Xinhui Shao)

llxiaobaichen@foxmail.com (Chen Li)

ztmath@163.com (Tie Zhang)

lichangjun16@126.com (Changjun Li)

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@Article{JCM-36-579, author = {Shao , XinhuiLi , ChenZhang , Tie and Li , Changjun}, title = {A Modified Preconditioner for Parameterized Inexact Uzawa Method for Indefinite Saddle Point Problems}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {4}, pages = {579--590}, abstract = {

The preconditioner for parameterized inexact Uzawa methods has been used to solve some indefinite saddle point problems. Firstly, we modify the preconditioner by making it more generalized, then we use theoretical analyses to show that the iteration method converges under certain conditions. Moreover, we discuss the optimal parameter and matrices based on these conditions. Finally, we propose two improved methods. Numerical experiments are provided to show the effectiveness of the modified preconditioner. All methods have fantastic convergence rates by choosing the optimal parameter and matrices.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1702-m2016-0665}, url = {http://global-sci.org/intro/article_detail/jcm/12306.html} }
TY - JOUR T1 - A Modified Preconditioner for Parameterized Inexact Uzawa Method for Indefinite Saddle Point Problems AU - Shao , Xinhui AU - Li , Chen AU - Zhang , Tie AU - Li , Changjun JO - Journal of Computational Mathematics VL - 4 SP - 579 EP - 590 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1702-m2016-0665 UR - https://global-sci.org/intro/article_detail/jcm/12306.html KW - Preconditioner, Inexact Uzawa method, Saddle point problems, Indefiniteness, Convergence. AB -

The preconditioner for parameterized inexact Uzawa methods has been used to solve some indefinite saddle point problems. Firstly, we modify the preconditioner by making it more generalized, then we use theoretical analyses to show that the iteration method converges under certain conditions. Moreover, we discuss the optimal parameter and matrices based on these conditions. Finally, we propose two improved methods. Numerical experiments are provided to show the effectiveness of the modified preconditioner. All methods have fantastic convergence rates by choosing the optimal parameter and matrices.

Shao , XinhuiLi , ChenZhang , Tie and Li , Changjun. (2018). A Modified Preconditioner for Parameterized Inexact Uzawa Method for Indefinite Saddle Point Problems. Journal of Computational Mathematics. 36 (4). 579-590. doi:10.4208/jcm.1702-m2016-0665
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