IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i9p815-d263730.html
   My bibliography  Save this article

An Efficient Iterative Method Based on Two-Stage Splitting Methods to Solve Weakly Nonlinear Systems

Author

Listed:
  • Abdolreza Amiri

    (Department of Mathematics, Razi University, Kermanshah 67149, Iran)

  • Mohammad Taghi Darvishi

    (Department of Mathematics, Razi University, Kermanshah 67149, Iran)

  • Alicia Cordero

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

  • Juan Ramón Torregrosa

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

Abstract

In this paper, an iterative method for solving large, sparse systems of weakly nonlinear equations is presented. This method is based on Hermitian/skew-Hermitian splitting (HSS) scheme. Under suitable assumptions, we establish the convergence theorem for this method. In addition, it is shown that any faster and less time-consuming two-stage splitting method that satisfies the convergence theorem can be replaced instead of the HSS inner iterations. Numerical results, such as CPU time, show the robustness of our new method. This method is easy, fast and convenient with an accurate solution.

Suggested Citation

  • Abdolreza Amiri & Mohammad Taghi Darvishi & Alicia Cordero & Juan Ramón Torregrosa, 2019. "An Efficient Iterative Method Based on Two-Stage Splitting Methods to Solve Weakly Nonlinear Systems," Mathematics, MDPI, vol. 7(9), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:815-:d:263730
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/9/815/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/9/815/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Márcia Gomes-Ruggiero & Véra Lopes & Julia Toledo-Benavides, 2008. "A globally convergent inexact Newton method with a new choice for the forcing term," Annals of Operations Research, Springer, vol. 157(1), pages 193-205, January.
    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. Min-Li Zeng & Guo-Feng Zhang, 2020. "On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations," Mathematics, MDPI, vol. 8(2), pages 1-17, February.

    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.

      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:gam:jmathe:v:7:y:2019:i:9:p:815-:d:263730. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      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.