Inexact Newton methods are variant of the Newton method in which each step satisfies only approximately the linear system (Ref. 1). The local convergence theory given by the authors of Ref. 1 and most of the results based on it consider the error terms as being provided only by the fact that the linear systems are not solved exactly. The few existing results for the general case (when some perturbed linear systems are considered, which in turn are

The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations $x_{k+1} = G(x_k )$ near a fixed point $x^ast$. Different conditions (ultimately on the magnitude of $G(x^ast)$) provide lower bounds for the convergence order of the process as a whole. In this paper, we consider only one such sequence and we characterize its high convergence orders in terms of some spectral elements of $G(x^ast)$; we obtain

A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method, which assumes perturbed Jacobians at each step. Its high convergence orders were characterized by Dennis and Moré [Math. Comp. 28 (1974), 549-560]. The inexact Newton method constitutes another such model, since it assumes that at each step the linear systems are only approximately solved; the high convergence orders of these iterations