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Notes on the Hermitian Positive Definite Solutions of a Matrix Equation

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  • Jing Li
  • Yuhai Zhang

Abstract

The nonlinear matrix equation, with is investigated. A fixed point theorem in partially ordered sets is proved. And then, by means of this fixed point theorem, the existence of a unique Hermitian positive definite solution for the matrix equation is derived. Some properties of the unique Hermitian positive definite solution are obtained. A residual bound of an approximate solution to the equation is evaluated. The theoretical results are illustrated by numerical examples.

Suggested Citation

  • Jing Li & Yuhai Zhang, 2014. "Notes on the Hermitian Positive Definite Solutions of a Matrix Equation," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, May.
    • Handle: RePEc:hin:jnljam:128249
    DOI: 10.1155/2014/128249
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