Convergence of Newton-like-iterative methods

Abstract

Newton-like methods in which the intermediate systems of linear equations are solved by iterative techniques are examined. By applying the theory of inexact Newton methods radius of convergence and rate of convergence results are easily obtained. The analysis is carried out in affine invariant terms. The results are applicable to cases where the underlying Newton-like method is, for example, a difference Newton-like or update-Newton method.