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On the semilocal convergence of the Halley method using recurrent functions

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An Erratum to this article was published on 08 September 2011

Abstract

We provide new semilocal convergence results for the Halley method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our sufficient convergence conditions can be weaker than before, where as the error bounds on the distances involved are finer. Our first approach uses a Kantorovich-type analysis. The second approach uses our new idea of recurrent functions. A comparison between the two approaches is also given.

A numerical example further validating the theoretical results is also provided in this study.

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Authors and Affiliations

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

    Ioannis K. Argyros

  2. Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju, 660-701, South Korea

    Yeol Je Cho

  3. Laboratoire de Mathématiques et Applications, Poitiers University, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962, Futuroscope Chasseneuil Cedex, France

    Saïd Hilout

Authors
  1. Ioannis K. Argyros
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  2. Yeol Je Cho
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  3. Saïd Hilout
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Correspondence to Ioannis K. Argyros.

Additional information

This work was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-313-C00050).

An erratum to this article can be found at http://dx.doi.org/10.1007/s12190-011-0512-1

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Argyros, I.K., Cho, Y.J. & Hilout, S. On the semilocal convergence of the Halley method using recurrent functions. J. Appl. Math. Comput. 37, 221–246 (2011). https://doi.org/10.1007/s12190-010-0431-6

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  • DOI: https://doi.org/10.1007/s12190-010-0431-6

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