Solutions and improved perturbation analysis for the matrix equation X-A^*X^-pA=Q (p>0)

2012/09/12 by Li, Jing
#65F10 #65F30 #65H05 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1209.2480

Abstract

In this paper the nonlinear matrix equation X-A^*X^-pA=Q with p>0 is investigated. We consider two cases of this equation: the case p>1 and the case 01, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbation estimate for the positive definite solution is derived. Explicit expressions of the condition number for the positive definite solution are given. In the case 0

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