Numerical Algorithms

, Volume 71, Issue 4, pp 811–826 | Cite as

Improved convergence analysis for Newton-like methods

  • Ángel Alberto Magreñán
  • Ioannis K. Argyros
Original Paper


We present a new semilocal convergence analysis for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these methods in cases not covered in earlier studies. The advantages of our approach include a more precise convergence analysis under the same computational cost on the Lipschitz constants involved. Applications are also given in this study to show that our estimates on the distances involved are tighter than the older ones.


Secant-type method Banach space Majorizing sequence Divided difference Local convergence Semilocal convergence 

Mathematics Subject Classification (2010)

65H10 65G99 65B05 65N30 47J25 47J05 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Ángel Alberto Magreñán
    • 1
  • Ioannis K. Argyros
    • 2
  1. 1.Escuela de IngenieríaUniversidad Internacional de La RiojaLogroñoSpain
  2. 2.Department of Mathematics SciencesCameron UniversityLawtonUSA

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