B. F. Svaiter

O. P. Ferreira, B. F. Svaiter

We prove that under semi-local assumptions, the inexact Newton method with a fixed relative residual error tolerance converges Q-linearly to a zero of the non-linear operator under consideration. Using this result we show that Newton method for minimizing a self-concordant function or to find a zero of an analytic function can be implemented with a fixed relative residual error tolerance. In the absence of errors, our analysis retrieve the classical Kantorovich Theorem on Newton method.

O. P. Ferreira, B. F. Svaiter

In this work we present a simplifyed proof of Kantorovich's Theorem on Newton's Method. This analysis uses a technique which has already been used for obtaining new extensions of this theorem.