A note on the quadratic convergence of the inexact Newton methods

Emil Cătinaş

doi:10.33993/jnaat292-662

Authors

Emil Cătinaş Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat292-662

Keywords:

nonlinear systems of equations in \(R^n\), inexact Newton methods, inexact and perturbed Newton methods, convergence orders, backward errors

Abstract views: 256

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.

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