  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.
