A note on the quadratic convergence of the inexact Newton methods

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Emil Cătinaş

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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