On the nonlinear matrix equation X+A*X-q A=Q(q≥1)

Authors:
Xuefeng Duan;Anping Liao
Affiliations:
School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, PR China and College of Mathematics and Econometrics, Hunan University, Changsha 410082, ...;College of Mathematics and Econometrics, Hunan University, Changsha 410082, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

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Abstract

The general nonlinear matrix equation X+A^*X^-^qA=Q(q=1) is investigated. Some sufficient conditions and necessary conditions for the existence of a (unique) positive definite solution are given. An iterative method is proposed to compute positive definite solutions.