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Computational Optimization and Applications

, Volume 42, Issue 2, pp 213–229 | Cite as

Kantorovich’s majorants principle for Newton’s method

Article

Abstract

We prove Kantorovich’s theorem on Newton’s method using a convergence analysis which makes clear, with respect to Newton’s method, the relationship of the majorant function and the non-linear operator under consideration. This approach enables us to drop out the assumption of existence of a second root for the majorant function, still guaranteeing Q-quadratic convergence rate and to obtain a new estimate of this rate based on a directional derivative of the derivative of the majorant function. Moreover, the majorant function does not have to be defined beyond its first root for obtaining convergence rate results.

Keywords

Kantorovich’s theorem Newton’s method 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.IME/UFGCampus IIGoiâniaBrazil
  2. 2.IMPAEstrada Dona CastorinaRio de JaneiroBrazil

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