Perturbation Analysis of the Nonlinear Matrix Equation X - ∑ i = 1 m ‍ A i * X p i A i = Q

Abstract

Consider the nonlinear matrix equation $X-{\sum }_{i=\mathrm{1}}^m\mathrm{‍}{A}_i^{\mathrm{*}}{X}^{p_i}{A}_i=Q$ with . Two perturbation bounds and the backward error of an approximate solution to the equation are derived. Explicit expressions of the condition number for the equation are obtained. The theoretical results are illustrated by numerical examples.