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Engwerda, J.C. (1993) On the Existence of a Positive Definite Solution of the Matrix Equation X + A^*X^-1A = I. Linear Algebra and Its Applications, 194, 91-108.
http://dx.doi.org/10.1016/0024-3795(93)90115-5

has been cited by the following article:

• TITLE: Positive Definite Solutions for the System of Nonlinear Matrix Equations X + A*Y-nA = I, Y + B*X-mB = I

  AUTHORS: Salah M. El-Sayed, Asmaa M. Al-Dubiban

  KEYWORDS: System of Nonlinear Matrix Equations, Iterative Methods, Monotonic Sequence, Positive Definite Matrices

  JOURNAL NAME: Applied Mathematics, Vol.5 No.13, July 15, 2014

  ABSTRACT: In this paper, some properties of the positive definite solutions for the nonlinear system of matrix equations X + A*Y-nA = I, Y + B*X-mB = I are derived. As a matter of fact, an effective iterative method to obtain the positive definite solutions of the system is established. These solutions are based on the convergence of monotone sequences of positive definite matrices. Moreover, the necessary and sufficient conditions for the existence of the positive definite solutions are obtained. Finally, some numerical results are given.