%0 Journal Article
%T On the Positive Definite Solutions of the Nonlinear Matrix Equation $ X-A^{*}X^{-s}A-B^{*}X^{-t}B=I$
%A Asmaa M. Al-Dubiban
%A Salah M. El-Sayed
%J Communications in Numerical Analysis
%D 2012
%I International scientific publication and consulting services (ISPACS)
%R 10.5899/2012/cna-00116
%X In the present paper, the positive definite solutions for the nonlinear matrix equation $X-A^{*}X^{-s}A-B^{*}X^{-t}B=I$, where $s,tin(0,1]$ are studied. The convergence of the proposed iterative methods are discussed. The necessary and sufficient conditions of the existence of positive definite solutions are derived. Finally, the results are illustrated by some numerical examples.
%K Nonlinear matrix equation
%K Iterative methods
%K Positive definite solution
%K Property
%K Existenc
%U http://www.ispacs.com/journals/cna/2012/cna-00116/article.pdf