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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
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    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).
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