# A note on the quadratic convergence of the inexact Newton methods

## Abstract

We show that a new sufficient condition for the convergence with q-order two of the inexact Newton iterates may be obtained by considering the normwise backward error of the approximate steps and a result on perturbed Newton methods. This condition is in fact equivalent to the characterization given by Dembo, Eisenstat and Steihaug.

## Authors

Emil Cătinaş
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

## Keywords

nonlinear system of equations in Rn; inexact Newton method; residual; local convergence; forcing term; q-convergence order.

## Cite this paper as:

E. Cătinaş, A note on the quadratic convergence of the inexact Newton methods, Rev. Anal. Numér. Théor. Approx., 29 (2000) no. 2, pp. 129-133.

Scanned paper.

1222-9024

2457-8126

MR

2457-8126