Perturbation Bounds for the Nonlinear Matrix Equation X + A~HX~(-1)A + B~HX~(-1)B = I

摘要

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, A~H denotes the complex conjugate transpose of the matrix A and / 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.