Numerical Algorithms

, Volume 55, Issue 4, pp 503–528 | Cite as

A convergence analysis for directional two-step Newton methods

  • Ioannis K. ArgyrosEmail author
  • Saïd Hilout
Original Paper


A semilocal convergence analysis for directional two-step Newton methods in a Hilbert space setting is provided in this study. Two different techniques are used to generate the sufficient convergence results, as well as the corresponding error bounds. The first technique uses our new idea of recurrent functions, whereas the second uses recurrent sequences. We also compare the results of the two techniques.


Directional two-step Newton method Hilbert space Nonlinear equation Lipschitz/center-Lipschitz condition Recurrent functions Recurrent sequences Newton–Kantorovich-type hypotheses 

AMS Subject Classifications

65H05 65H10 49M15 


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Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.Department of Mathematics SciencesCameron UniversityLawtonUSA
  2. 2.Laboratoire de Mathématiques et ApplicationsPoitiers UniversityFuturoscope Chasseneuil CedexFrance

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