IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v361y2019icp421-429.html
   My bibliography  Save this article

Accelerating the shift-splitting iteration algorithm

Author

Listed:
  • Li, Zhizhi
  • Chu, Risheng
  • Zhang, Huai

Abstract

The dazzling property of shift-splitting iteration method is unconditional convergence for any parameters and Anderson mixing as a simple and classic method can greatly speed up convergence of fix point iterations. Inheriting the merits of them, we propose an accelerated preconditioning shift-splitting algorithm for generalized saddle point problems. Then, we verify its unconditional convergence. Besides, we discuss the spectrum distribution of iteration matrix and then provide the relationship of optimal parameters involved. Finally, numerical experiments underline its superiority both as a solver and preconditioner.

Suggested Citation

  • Li, Zhizhi & Chu, Risheng & Zhang, Huai, 2019. "Accelerating the shift-splitting iteration algorithm," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 421-429.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:421-429
    DOI: 10.1016/j.amc.2019.05.056
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319304588
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.05.056?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. 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.
    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. Ke, Yi-Fen & Ma, Chang-Feng, 2017. "The dimensional splitting iteration methods for solving saddle point problems arising from time-harmonic eddy current models," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 146-164.
    3. Li, Chengliang & Ma, Changfeng & Xu, Xiaofang, 2020. "A class of efficient parameterized shift-splitting preconditioners for block two-by-two linear systems," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    4. Ling, Si-Tao & Liu, Qing-Bing, 2017. "New local generalized shift-splitting preconditioners for saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 58-67.
    5. Huang, Na & Ma, Chang-Feng & Xie, Ya-Jun, 2015. "An inexact relaxed DPSS preconditioner for saddle point problem," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 431-447.

    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:361:y:2019:i:c:p:421-429. 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.