IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i21p4436-d1267810.html
   My bibliography  Save this article

On the Iterative Methods for the Solution of Three Types of Nonlinear Matrix Equations

Author

Listed:
  • Ivan G. Ivanov

    (Faculty of Economics and Business Administration, Sofia University “St.Kl.Ohridski”, 1000 Sofia, Bulgaria
    These authors contributed equally to this work.)

  • Hongli Yang

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
    These authors contributed equally to this work.)

Abstract

In this paper, we investigate the iterative methods for the solution of different types of nonlinear matrix equations. More specifically, we consider iterative methods for the minimal nonnegative solution of a set of Riccati equations, a nonnegative solution of a quadratic matrix equation, and the maximal positive definite solution of the equation X + A ∗ X − 1 A = Q . We study the recent iterative methods for computing the solution to the above specific type of equations and propose more effective modifications of these iterative methods. In addition, we make comments and comparisons of the existing methods and show the effectiveness of our methods by illustration examples.

Suggested Citation

  • Ivan G. Ivanov & Hongli Yang, 2023. "On the Iterative Methods for the Solution of Three Types of Nonlinear Matrix Equations," Mathematics, MDPI, vol. 11(21), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4436-:d:1267810
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/21/4436/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/21/4436/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Qing Yang & Xiaojing Wang & Xiwang Cheng & Bo Du & Yuxiao Zhao, 2023. "Positive Periodic Solution for Neutral-Type Integral Differential Equation Arising in Epidemic Model," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    2. Guan, Jinrui, 2019. "Modified alternately linearized implicit iteration method for M-matrix algebraic Riccati equations," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 442-448.
    3. Ma, Li & Li, Yujing & Zhu, Quanxin, 2023. "Stability analysis for a class of stochastic delay nonlinear systems driven by G-Lévy Process," Statistics & Probability Letters, Elsevier, vol. 195(C).
    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. Zhengqi Ma & Shoucheng Yuan & Kexin Meng & Shuli Mei, 2023. "Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    2. Zhao Li & Chen Peng, 2023. "Dynamics and Embedded Solitons of Stochastic Quadratic and Cubic Nonlinear Susceptibilities with Multiplicative White Noise in the Itô Sense," Mathematics, MDPI, vol. 11(14), pages 1-11, July.
    3. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "The balanced split step theta approximations of stochastic neutral Hopfield neural networks with time delay and Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 455(C).

    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:11:y:2023:i:21:p:4436-:d:1267810. 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.