Volume 7, Issue 1
A New Uzawa-Type Iteration Method for Non-Hermitian Saddle-Point Problems

Yan Dou, Ai-Li Yang & Yu-Jiang Wu

East Asian J. Appl. Math., 7 (2017), pp. 211-226.

Published online: 2018-02

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  • Abstract

Based on a preconditioned shift-splitting of the (1, 1)-block of non-Hermitian saddle-point matrix and the Uzawa iteration method, we establish a new Uzawa-type iteration method. The convergence properties of this iteration method are analyzed. In addition, based on this iteration method, a preconditioner is proposed. The spectral properties of the preconditioned saddle-point matrix are also analyzed. Numerical results are presented to verify the robustness and the efficiency of the new iteration method and the preconditioner.

  • Keywords

Saddle-point problems, Uzawa method, preconditioned shift-splitting, convergence, preconditioner.

  • AMS Subject Headings

65F08, 65F10, 65F20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-211, author = {}, title = {A New Uzawa-Type Iteration Method for Non-Hermitian Saddle-Point Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {1}, pages = {211--226}, abstract = {

Based on a preconditioned shift-splitting of the (1, 1)-block of non-Hermitian saddle-point matrix and the Uzawa iteration method, we establish a new Uzawa-type iteration method. The convergence properties of this iteration method are analyzed. In addition, based on this iteration method, a preconditioner is proposed. The spectral properties of the preconditioned saddle-point matrix are also analyzed. Numerical results are presented to verify the robustness and the efficiency of the new iteration method and the preconditioner.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.290816.130117a}, url = {http://global-sci.org/intro/article_detail/eajam/10744.html} }
TY - JOUR T1 - A New Uzawa-Type Iteration Method for Non-Hermitian Saddle-Point Problems JO - East Asian Journal on Applied Mathematics VL - 1 SP - 211 EP - 226 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.290816.130117a UR - https://global-sci.org/intro/article_detail/eajam/10744.html KW - Saddle-point problems, Uzawa method, preconditioned shift-splitting, convergence, preconditioner. AB -

Based on a preconditioned shift-splitting of the (1, 1)-block of non-Hermitian saddle-point matrix and the Uzawa iteration method, we establish a new Uzawa-type iteration method. The convergence properties of this iteration method are analyzed. In addition, based on this iteration method, a preconditioner is proposed. The spectral properties of the preconditioned saddle-point matrix are also analyzed. Numerical results are presented to verify the robustness and the efficiency of the new iteration method and the preconditioner.

Yan Dou, Ai-Li Yang & Yu-Jiang Wu. (2020). A New Uzawa-Type Iteration Method for Non-Hermitian Saddle-Point Problems. East Asian Journal on Applied Mathematics. 7 (1). 211-226. doi:10.4208/eajam.290816.130117a
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