Numerical Algorithms

, Volume 70, Issue 2, pp 377–392

On the semilocal convergence of a three steps Newton-type iterative process under mild convergence conditions

Original Paper

DOI: 10.1007/s11075-014-9952-7

Cite this article as:
Hernández-Verón, M.A. & Martínez, E. Numer Algor (2015) 70: 377. doi:10.1007/s11075-014-9952-7

Abstract

In this paper the semilocal convergence for an alternative to the three steps Newton’s method with frozen derivative is presented. We analyze the generalization of convergence conditions given by w-conditioned non-decreasing functions instead of the first derivative Lipschitz or Holder continuous given by other authors. A nonlinear integral equation of mixed Hammerstein type is considered for illustrating the new theoretical results obtained in this paper, where previous results can not be satisfied.

Keywords

Nonlinear equations Order of convergence Iterative methods Semilocal convergence Hammerstein equation 

Mathematics Subject Classification (2010)

47H99 65H10 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics and ComputationUniversity of La RiojaLogroñoSpain
  2. 2.Instituto de Matemática Pura y AplicadaUniversidad Politécnica de ValenciaValenciaSpain

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