Local convergence comparison between two novel sixth order methods for solving equations

Santhosh George, and Ioannis K. Argyros. "Local convergence comparison between two novel sixth order methods for solving equations." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 18 (2019): 5-19. <http://eudml.org/doc/296826>.

@article{SanthoshGeorge2019,
abstract = {The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated to present convergence analysis based only on the first derivative. Numerical examples where the convergence criteria are tested are provided. It turns out that in these examples the criteria in the earlier works are not satisfied, so these results cannot be used to solve equations but our results can be used.},
author = {Santhosh George, Ioannis K. Argyros},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {Jarratt-like method; sixth order of convergence; local convergence; Banach space; Frechet-derivative},
language = {eng},
pages = {5-19},
title = {Local convergence comparison between two novel sixth order methods for solving equations},
url = {http://eudml.org/doc/296826},
volume = {18},
year = {2019},
}

TY - JOUR
AU - Santhosh George
AU - Ioannis K. Argyros
TI - Local convergence comparison between two novel sixth order methods for solving equations
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2019
VL - 18
SP - 5
EP - 19
AB - The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated to present convergence analysis based only on the first derivative. Numerical examples where the convergence criteria are tested are provided. It turns out that in these examples the criteria in the earlier works are not satisfied, so these results cannot be used to solve equations but our results can be used.
LA - eng
KW - Jarratt-like method; sixth order of convergence; local convergence; Banach space; Frechet-derivative
UR - http://eudml.org/doc/296826
ER -