Hermitian Positive Definite Solutions of the Matrix Equation $X A^*X^{-q}A=Q~(q\geq 1)$
Received:October 17, 2007  Revised:May 21, 2008
Key Word: nonlinear matrix equations   positive definite solution   iterative method.  
Fund ProjectL:the Natural Science Foundation of Hunan Province (No.09JJ6012).
Author NameAffiliation
LIU Wei Department of Information and Computing Science, Changsha University, Hunan 410003, China
College of Mathematics and Econometrics, Hunan University, Hunan 410082, China 
LIAO An Ping College of Mathematics and Econometrics, Hunan University, Hunan 410082, China
 
DUAN Xue Feng College of Mathematics and Econometrics, Hunan University, Hunan 410082, China
School of Mathematics & Computational Science, Guilin University of Electronic Technology, Guangxi 541004, China 
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Abstract:
      In this paper, Hermitian positive definite solutions of the nonlinear matrix equation $X A^*X^{-q}A=Q\ (q\geq 1)$ are studied. Some new necessary and sufficient conditions for the existence of solutions are obtained. Two iterative methods are presented to compute the smallest and the quasi largest positive definite solutions, and the convergence analysis is also given. The theoretical results are illustrated by numerical examples.
Citation:
DOI:10.3770/j.issn:1000-341X.2009.05.008
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