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

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

El-Sayed, S. and Al-Dubiban, A. (2014) Positive Definite Solutions for the System of Nonlinear Matrix Equations X + A*Y-nA = I, Y + B*X-mB = I. Applied Mathematics, 5, 1977-1987. doi: 10.4236/am.2014.513193.

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