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

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Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. Department of Mathematical Sciences, Cameron University, Lawton, OK , 73505, USA

    I. K. Argyros

  2. Center on Mathematical Modelling, Escuela Politécnica Nacional, Quito, Ecuador

    D. González

Authors
  1. I. K. Argyros
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  2. D. González
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Correspondence to D. González.

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Argyros, I.K., González, D. Extending the applicability of Newton’s method by improving a local result due to Dennis and Schnabel. SeMA 63, 53–63 (2014). https://doi.org/10.1007/s40324-014-0011-z

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  • DOI: https://doi.org/10.1007/s40324-014-0011-z

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