@article{Argyros_Ren_2013, title={Convergence of Halley’s method under centered Lipschitz condition on the second Fréchet derivative}, volume={42}, url={https://ictp.acad.ro/jnaat/journal/article/view/2013-vol42-no1-art1}, DOI={10.33993/jnaat421-979}, abstractNote={<pre>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. <br>We assume that the second Fréchet-derivative satisfies a centered Lipschitz condition. <br>Numerical examples are used to show that the new convergence criteria are satisfied but earlier ones are not satisfied.</pre>}, number={1}, journal={Rev. Anal. Numér. Théor. Approx.}, author={Argyros, Ioannis K. and Ren, Hongmin}, year={2013}, month={Feb.}, pages={3–20} }