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

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References

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http://dx.doi.org/10.1016/0024-3795(90)90005-W

[2] Lancaster, P. and Rodman, L. (1995) Algebraic Riccati Equations. Oxford Science, Oxford.

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[4] Engwerda, J.C. (1993) On the Existence of a Positive Definite Solution of the Matrix Equation *X* + *A ^{*}X^{-1}A* =

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[5] Hasanov, V.I. and Ivanov, I.G. (2004) Solutions and Perturbation Estimates for the Matrix Equations *X* ±*A ^{*}X^{-n}A* =

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[6] Hasanov, V.I. and El-Sayed, S.M. (2006) On the Positive Definite Solutions of Nonlinear Matrix Equation *X* + *A ^{*}X^{-δ}A* =

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[11] Czornik, A. and Swierniak, A. (2001) Upper Bounds on the Solution of Coupled Algebraic Riccati Equation. Journal of Inequalities and Applications, 6, 373-385.

[12] Mukaidani, H., Yamamoto, S. and Yamamoto, T. (2008) A Numerical Algorithm for Finding Solution of Cross-Coupled Algebraic Riccati Equations. IEICE Transactions, 91, 682-685.

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[13] Al-Dubiban, A.M. (2008) Iterative Algorithms for Computing the Positive Definite Solutions for Nonlinear Matrix Equations. Ph.D. Thesis, Riyadh University for Girls, Riyadh.

[14] Al-Dubiban, A.M. (2012) Iterative Algorithm for Solving a System of Nonlinear Matrix Equations. Journal of Applied Mathematics, 2012, Article ID: 461407.

[15] Al-Dubiban, A.M. (2013) On the Iterative Method for the System of Nonlinear Matrix Equations. Abstract and Applied Analysis, 2013, Article ID: 685753.