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Solutions and Improved Perturbation Analysis for the Matrix Equation

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  • Jing Li

Abstract

The nonlinear matrix equation with is investigated. We consider two cases of this equation: the case and the case In the case , a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbation estimate for the positive definite solution is derived. Explicit expressions of the condition number for the positive definite solution are given. In the case , a new sharper perturbation bound for the unique positive definite solution is derived. A new backward error of an approximate solution to the unique positive definite solution is obtained. The theoretical results are illustrated by numerical examples.

Suggested Citation

  • Jing Li, 2013. "Solutions and Improved Perturbation Analysis for the Matrix Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, June.
    • Handle: RePEc:hin:jnlaaa:575964
    DOI: 10.1155/2013/575964
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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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