Convergence of Halley's method under centered Lipschitz condition on the second Fréchet derivative

Authors

  • Ioannis K. Argyros Cameron University, USA
  • Hongmin Ren Hangzhou Polytechnic, China

DOI:

https://doi.org/10.33993/jnaat421-979

Keywords:

Halley's method, Fréchet-derivative, Banach space, semi-local convergence, Frechet derivative, centered Lipschitz condition
Abstract views: 295

Abstract

We present a semi-local as well as a local convergence analysis of Halley's method for approximating a locally unique solution of a nonlinear equation in a Banach space setting.
We assume that the second Fréchet-derivative satisfies a centered Lipschitz condition.
Numerical examples are used to show that the new convergence criteria are satisfied but earlier ones are not satisfied.

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References

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Published

2013-02-01

How to Cite

Argyros, I. K., & Ren, H. (2013). Convergence of Halley’s method under centered Lipschitz condition on the second Fréchet derivative. Rev. Anal. Numér. Théor. Approx., 42(1), 3–20. https://doi.org/10.33993/jnaat421-979

Issue

Vol. 42 No. 1 (2013)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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