Difference equations and local convergence of inexact Newton methods

Abstract

In this paper, some observations on local convergence of inexact Newton methods are given. The basic perturbation result concerning difference equations due to Perron and Ostrowski is used to show the local convergence of various inexact Newton methods, i.e., methods which the Newton equations F′( x k ) s k = − F( x k ), x k+1 = x k + s k , x 0 − given, s