Open Access
2015 Positive Definite Solutions of the Matrix Equation Xr-i=1mAiX-δiAi=I
Asmaa M. Al-Dubiban
Abstr. Appl. Anal. 2015: 1-8 (2015). DOI: 10.1155/2015/473965


We investigate the nonlinear matrix equation Xr-i=1mAiX-δiAi=I, where r is a positive integer and δi(0,1],fori=1,2,…,m. We establish necessary and sufficient conditions for the existence of positive definite solutions of this equation. A sufficient condition for the equation to have a unique positive definite solution is established. An iterative algorithm is provided to compute the positive definite solutions for the equation and error estimate. Finally, some numerical examples are given to show the effectiveness and convergence of this algorithm.


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Asmaa M. Al-Dubiban. "Positive Definite Solutions of the Matrix Equation Xr-i=1mAiX-δiAi=I." Abstr. Appl. Anal. 2015 1 - 8, 2015.


Published: 2015
First available in Project Euclid: 17 August 2015

zbMATH: 1314.65062
MathSciNet: MR3372884
Digital Object Identifier: 10.1155/2015/473965

Rights: Copyright © 2015 Hindawi

Vol.2015 • 2015
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