Perturbation bounds for the nonlinear matrix equation X + A HX -1 A + B HX -1 B = I

Abstract

In this paper we make a complete perturbation analysis of the nonlinear matrix equation X + A HX -1 A + B HX -1 B = I, where A and B are square complex matrices, denotes the complex conjugate transpose of the matrix A and I is the identity matrix. We obtain local (first order) perturbation bounds and a non-local perturbation bound for the solution to the equation. The perturbation bounds allow to derive condition and accuracy estimates for the computed solution, when using a stable numerical algorithm to solve the equation. © 2012 Springer-Verlag.