IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i14p2416-d860437.html
   My bibliography  Save this article

New Criterions-Based H -Tensors for Testing the Positive Definiteness of Multivariate Homogeneous Forms

Author

Listed:
  • Dongjian Bai

    (College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China)

  • Feng Wang

    (College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China)

Abstract

Positive definite homogeneous multivariate forms play an important role in polynomial problems and medical imaging, and the definiteness of forms can be tested using structured tensors. In this paper, we state the equivalence between the positive definite multivariate forms and the corresponding tensors, and explain the connection between the positive definite tensors with H -tensors. Then, based on the notion of diagonally dominant tensors, some criteria for H -tensors are presented. Meanwhile, with these links, we provide an iterative algorithm to test the positive definiteness of multivariate homogeneous forms and prove its validity theoretically. The advantages of the obtained results are illustrated by some numerical examples.

Suggested Citation

  • Dongjian Bai & Feng Wang, 2022. "New Criterions-Based H -Tensors for Testing the Positive Definiteness of Multivariate Homogeneous Forms," Mathematics, MDPI, vol. 10(14), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2416-:d:860437
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/14/2416/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/14/2416/
    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:10:y:2022:i:14:p:2416-:d:860437. 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.