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On the Iterative Method for the System of Nonlinear Matrix Equations

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  • Asmaa M. Al-Dubiban

Abstract

The positive definite solutions for the system of nonlinear matrix equations X + A∗Y−nA = I, Y + B∗X−mB = I are considered, where n, m are two positive integers and A, B are nonsingular complex matrices. Some sufficient conditions for the existence of positive definite solutions for the system are derived. Under some conditions, an iterative algorithm for computing the positive definite solutions for the system is proposed. Also, the estimation of the error is obtained. Finally, some numerical examples are given to show the efficiency of the proposed iterative algorithm.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:685753
    DOI: 10.1155/2013/685753
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    References listed on IDEAS

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    1. Feng Yin & Guang-Xin Huang, 2012. "An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations AXB = E,CXD = F," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. 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).

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