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The Inversion‐Free Iterative Methods for Solving the Nonlinear Matrix Equation X + AHX−1A + BHX−1B = I

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  • Na Huang
  • Changfeng Ma

Abstract

We present two inversion‐free iterative methods for computing the maximal positive definite solution of the equation X + AHX−1A + BHX−1B = I. We prove that the sequences generated by the two iterative schemes are monotonically increasing and bounded above. We also present some numerical results to compare our proposed methods with some previously developed inversion‐free techniques for solving the same matrix equation.

Suggested Citation

  • Na Huang & Changfeng Ma, 2013. "The Inversion‐Free Iterative Methods for Solving the Nonlinear Matrix Equation X + AHX−1A + BHX−1B = I," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:843785
    DOI: 10.1155/2013/843785
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    References listed on IDEAS

    as
    1. Asmaa M. Al-Dubiban, 2012. "Iterative Algorithm for Solving a System of Nonlinear Matrix Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, December.
    2. Asmaa M. Al-Dubiban, 2013. "On the Iterative Method for the System of Nonlinear Matrix Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, March.
    3. Asmaa M. Al-Dubiban, 2013. "On the Iterative Method for the System of Nonlinear Matrix Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Asmaa M. Al-Dubiban, 2012. "Iterative Algorithm for Solving a System of Nonlinear Matrix Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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