IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v356y2019icp479-501.html
   My bibliography  Save this article

The general inner-outer iteration method based on regular splittings for the PageRank problem

Author

Listed:
  • Tian, Zhaolu
  • Liu, Yong
  • Zhang, Yan
  • Liu, Zhongyun
  • Tian, Maoyi

Abstract

In this paper, combined the regular splittings of the coefficient matrix I−αP with the inner-outer iteration framework [9], a general inner-outer (GIO) iteration method is presented for solving the PageRank problem. Firstly, the AOR and modified AOR (MAOR) methods for solving the PageRank problem are constructed, and several comparison results are also given. Next, the GIO iteration scheme is developed, and its overall convergence is analyzed in detail. Furthermore, the preconditioner derived from the GIO iteration can be used to accelerate the Krylov subspace methods, such as GMRES method. Finally, some numerical experiments on several PageRank problems are provided to illustrate the efficiency of the proposed algorithm.

Suggested Citation

  • Tian, Zhaolu & Liu, Yong & Zhang, Yan & Liu, Zhongyun & Tian, Maoyi, 2019. "The general inner-outer iteration method based on regular splittings for the PageRank problem," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 479-501.
    • Handle: RePEc:eee:apmaco:v:356:y:2019:i:c:p:479-501
    DOI: 10.1016/j.amc.2019.02.066
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319301766
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.02.066?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. Shen, Zhao-Li & Huang, Ting-Zhu & Carpentieri, Bruno & Gu, Xian-Ming & Wen, Chun, 2017. "An efficient elimination strategy for solving PageRank problems," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 111-122.
    2. Huang, Na & Ma, Chang-Feng, 2015. "Parallel multisplitting iteration methods based on M-splitting for the PageRank problem," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 337-343.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shen, Zhao-Li & Su, Meng & Carpentieri, Bruno & Wen, Chun, 2022. "Shifted power-GMRES method accelerated by extrapolation for solving PageRank with multiple damping factors," Applied Mathematics and Computation, Elsevier, vol. 420(C).

    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. Del Corso, Gianna M. & Romani, Francesco, 2019. "Adaptive nonnegative matrix factorization and measure comparisons for recommender systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 164-179.
    2. Shen, Zhao-Li & Su, Meng & Carpentieri, Bruno & Wen, Chun, 2022. "Shifted power-GMRES method accelerated by extrapolation for solving PageRank with multiple damping factors," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    3. Yajun Xie & Lihua Hu & Changfeng Ma, 2023. "A Parameterized Multi-Splitting Iterative Method for Solving the PageRank Problem," Mathematics, MDPI, vol. 11(15), pages 1-12, July.
    4. Aleja, David & Criado, Regino & García del Amo, Alejandro J. & Pérez, Ángel & Romance, Miguel, 2019. "Non-backtracking PageRank: From the classic model to hashimoto matrices," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 283-291.

    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:356:y:2019:i:c:p:479-501. 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.