Open Access
2013 On the Positive Definite Solutions of a Nonlinear Matrix Equation
Panpan Liu, Shugong Zhang, Qingchun Li
J. Appl. Math. 2013: 1-6 (2013). DOI: 10.1155/2013/676978


The positive definite solutions of the nonlinear matrix equation Xs+Af(X)A=Q are discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived. Then, the uniqueness of the Hermitian positive definite solution is studied based on an iterative method proposed in this paper. Lastly the perturbation analysis for this equation is discussed.


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Panpan Liu. Shugong Zhang. Qingchun Li. "On the Positive Definite Solutions of a Nonlinear Matrix Equation." J. Appl. Math. 2013 1 - 6, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1268.15013
MathSciNet: MR3056214
Digital Object Identifier: 10.1155/2013/676978

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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