SeMA Journal

, Volume 63, Issue 1, pp 53–63 | Cite as

Extending the applicability of Newton’s method by improving a local result due to Dennis and Schnabel

  • I. K. Argyros
  • D. GonzálezEmail author


We present a tighter local convergence result for Newton’s method under generalized conditions of Kantorovich type than the one given by Dennis and Schnabel (Numerical methods for unconstrained optimization and nonlinear equations. SIAM, Philadelphia, 1996) and by Ezquerro et al. (J Comput Appl Math 236:2246–2258, 2012) by using more precise majorizing functions and sequences. These improvements are obtained under the same computational cost as in the earlier studies. Numerical examples are also provided to show that the new convergence radii are larger and the new error bounds are tighter than the older ones.


Newton’s method Local convergence Order convergence 

Mathematics Subject Classification (2000)

47H99 65J15 



This scientific work has been supported by the ‘Proyecto Prometeo’ of the Ministry of Higher Education Science, Technology and Innovation of the Republic of Ecuador.


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Copyright information

© Sociedad Española de Matemática Aplicada 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesCameron UniversityLawtonUSA
  2. 2.Center on Mathematical ModellingEscuela Politécnica NacionalQuitoEcuador

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