A Perturbation Analysis for Nonlinear Selfadjoint Operator Equations
André C. M. Ran, Martine Reurings, Leiba Rodman · SIAM Journal on Matrix Analysis and Applications · 2006
Perturbation analysis, including perturbation bounds, is developed for nonlinear operator equations of the form $X = Q \pm A^* F(X) A$, under perturbations of the given operators Q (which is assumed to be positive definite) and A and of the given operator function F(X) which takes self-adjoint operator values. Stability of fixed points under suitable map perturbations serves as the main technical tool. More detailed analysis is provided in the particular cases where F(X) is a power map.