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
Cite this paper
El-Sayed, S. and Al-Dubiban, A. (2014) Positive Definite Solutions for the System of Nonlinear Matrix Equations X
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