On Newton's method using recurrent functions under hypotheses up to the second Fréchet derivative

Authors

  • Ioannis K. Argyros Cameron University, USA
  • Saïd Hilout Poitiers University, France

DOI:

https://doi.org/10.33993/jnaat412-972

Keywords:

Newton's method, recurrent functions, Banach space, semilocal convergence, Fréchet-derivative, majorizing sequence, Lipschitz/center-Lipschitz conditions, radius of convergence
Abstract views: 229

Abstract

We provide semilocal result for the convergence of Newton method to a locally unique solution of an equation in a Banach space setting using hypotheses up to the second Fréchet-derivatives and our new idea of recurrent functions. The advantages of such conditions over earlier ones in some cases are: finer bounds on the distances involved, and a better information on the location of the solution.

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References

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Published

2012-08-01

How to Cite

Argyros, I. K., & Hilout, S. (2012). On Newton’s method using recurrent functions under hypotheses up to the second Fréchet derivative. Rev. Anal. Numér. Théor. Approx., 41(2), 99–113. https://doi.org/10.33993/jnaat412-972

Issue

Vol. 41 No. 2 (2012)

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Articles

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