Geodesic
On the local convergence of Newton-like methods with fourth and fifth order of convergence under hypotheses only on the first Fréchet derivative
Novi Sad Journal of Mathematics, Tome 47 (2017) no. 1.

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We present a local convergence analysis of several Newton-like methods with fourth and fifth order of convergence in order to approximate a locally unique solution of an equation in Banach space setting. Earlier studies have used hypotheses up to the fifth derivative although only the first derivative appears in the definition of these methods. In this study we only use the hypothesis on the first derivative. This way we expand the applicability of these methods. Moreover, we provide a radius of convergence, a uniqueness ball and computable error bounds based on Lipschitz constants. Numerical examples computing the radii of the convergence balls as well as examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.
Publié le :
DOI : 10.30755/NSJOM.02360
Classification : 65D10, 65D99, 65E99
Keywords: Newton-type methods, Banach space, fourth and fifth convergence order methods, local convergence, Frechet-derivative 
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Ioannis K. Argyros; P. Jidesh; Santhosh George. On the local convergence of Newton-like methods with fourth and fifth order
of convergence under hypotheses only on the first Fréchet derivative. Novi Sad Journal of Mathematics, Tome 47 (2017) no. 1. doi : 10.30755/NSJOM.02360. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.02360/

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