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2012 Iterative Algorithm for Solving a System of Nonlinear Matrix Equations
Asmaa M. Al-Dubiban
J. Appl. Math. 2012: 1-15 (2012). DOI: 10.1155/2012/461407


We discuss the positive definite solutions for the system of nonlinear matrix equations X A Y n A = I and Y B X m B = I , where n , m are two positive integers. Some properties of solutions are studied, and the necessary and sufficient conditions for the existence of positive definite solutions are given. An iterative algorithm for obtaining positive definite solutions of the system is proposed. Moreover, the error estimations are found. Finally, some numerical examples are given to show the efficiency of the proposed iterative algorithm.


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Asmaa M. Al-Dubiban. "Iterative Algorithm for Solving a System of Nonlinear Matrix Equations." J. Appl. Math. 2012 1 - 15, 2012.


Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1268.65058
MathSciNet: MR3000282
Digital Object Identifier: 10.1155/2012/461407

Rights: Copyright © 2012 Hindawi


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