IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i7p1080-d1620523.html
   My bibliography  Save this article

An Accelerated Sixth-Order Procedure to Determine the Matrix Sign Function Computationally

Author

Listed:
  • Shuai Wang

    (Foundation Department, Changchun Guanghua University, Changchun 130033, China)

  • Ziyang Wang

    (Sydney Smart Technology College, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Wu Xie

    (Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration (Hebei Center of Marine Geological Resources Survey), Qinhuangdao 066000, China)

  • Yunfei Qi

    (Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration (Hebei Center of Marine Geological Resources Survey), Qinhuangdao 066000, China)

  • Tao Liu

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

Abstract

The matrix sign function has a key role in several applications in numerical linear algebra. This paper presents a novel iterative approach with a sixth order of convergence to efficiently compute this function. The scheme is constructed via the employment of a nonlinear equations solver for simple roots. Then, the convergence of the extended matrix procedure is investigated to demonstrate the sixth rate of convergence. Basins of attractions for the proposed solver are given to show its global convergence behavior as well. Finally, the numerical experiments demonstrate the effectiveness of our approach compared to classical methods.

Suggested Citation

  • Shuai Wang & Ziyang Wang & Wu Xie & Yunfei Qi & Tao Liu, 2025. "An Accelerated Sixth-Order Procedure to Determine the Matrix Sign Function Computationally," Mathematics, MDPI, vol. 13(7), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1080-:d:1620523
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/7/1080/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/7/1080/
    Download Restriction: no
    ---><---

    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:13:y:2025:i:7:p:1080-:d:1620523. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.