Local Convergence of Inexact Newton Methods

A simple affine invariant condition which ensures local convergence of inexact Newton methods is provided. This condition is closely linked with the characterization of superlinear convergence given by Dennis and Moré. Radius of convergence and rate of convergence results are derived, and we show the theory is, in some sense, sharp. We apply the theory to various inexact Newton methods, including difference Newton-like methods and the general Newton-like method in which the iterates are perturbed by rounding errors in the computation.