IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v265y2015icp414-430.html
   My bibliography  Save this article

A new generalized parameterized inexact Uzawa method for solving saddle point problems

Author

Listed:
  • Dai, Lifang
  • Liang, Maolin
  • Fan, Hongtao

Abstract

Recently, Bai, Parlett and Wang presented a class of parameterized inexact Uzawa (PIU) methods for solving saddle point problems (Bai et al., 2005). In this paper, we develop a new generalized PIU method for solving both nonsingular and singular saddle point problems. The necessary and sufficient conditions of the convergence (semi-convergence) for solving nonsingular (singular) saddle point problems are derived. Meanwhile, the characteristic of eigenvalues of the iteration matrix corresponding to the above iteration method is discussed. We further show that the generalized PIU-type method proposed in this paper has a wider convergence (semi-convergence) region than some classical Uzawa methods, such as the inexact Uzawa method, the SOR-like method, the GSOR method and so on. Finally, numerical examples are given to illustrate the feasibility and efficiency of this method.

Suggested Citation

  • Dai, Lifang & Liang, Maolin & Fan, Hongtao, 2015. "A new generalized parameterized inexact Uzawa method for solving saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 414-430.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:414-430
    DOI: 10.1016/j.amc.2015.05.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315006384
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.05.021?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yang, Ai-Li & Li, Xu & Wu, Yu-Jiang, 2015. "On semi-convergence of the Uzawa–HSS method for singular saddle-point problems," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 88-98.
    2. Fan, Hong-tao & Zhu, Xin-yun & Zheng, Bing, 2015. "On semi-convergence of a class of relaxation methods for singular saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 68-80.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huang, Zheng-Ge & Wang, Li-Gong & Xu, Zhong & Cui, Jing-Jing, 2017. "The generalized modified shift-splitting preconditioners for nonsymmetric saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 95-118.
    2. Cao, Yang & Yi, Shi-Chao, 2016. "A class of Uzawa-PSS iteration methods for nonsingular and singular non-Hermitian saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 41-49.
    3. Miao, Shu-Xin, 2017. "A new Uzawa-type method for saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 300(C), pages 95-102.
    4. Chen, Cai-Rong & Ma, Chang-Feng, 2015. "A generalized shift-splitting preconditioner for singular saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 947-955.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:414-430. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.