The relationship between the models of perturbed Newton iterations, with applications

Abstract The quasi‐Newton method and the inexact Newton method are classical models of Newton iterates which take into account certain error terms. We have recently introduced the inexact perturbed Newton method, which takes into account all the possible sources of perturbations. We show that these models are in fact equivalent, in the sense that each one may be used to characterize the high convergence orders of the other two. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)