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Latest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations

Author

Listed:
  • Sourav Shil
  • Hemant Kumar Nashine
  • Ali Jaballah

Abstract

In this work, the following system of nonlinear matrix equations is considered, X1+A∗X1−1A+B∗X2−1B=I and X2+C∗X2−1C+D∗X1−1D=I, where A,B,C, and D are arbitrary n×n matrices and I is the identity matrix of order n. Some conditions for the existence of a positive-definite solution as well as the convergence analysis of the newly developed algorithm for finding the maximal positive-definite solution and its convergence rate are discussed. Four examples are also provided herein to support our results.

Suggested Citation

  • Sourav Shil & Hemant Kumar Nashine & Ali Jaballah, 2021. "Latest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations," Journal of Mathematics, Hindawi, vol. 2021, pages 1-22, August.
    • Handle: RePEc:hin:jjmath:2667885
    DOI: 10.1155/2021/2667885
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    Cited by:

    1. Malik Zaka Ullah, 2021. "A New Inversion-Free Iterative Scheme to Compute Maximal and Minimal Solutions of a Nonlinear Matrix Equation," Mathematics, MDPI, vol. 9(23), pages 1-7, November.

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