Extended convergence analysis of the Newton–Potra method under weak conditions
Volume 48 / 2021
Applicationes Mathematicae 48 (2021), 101-110
MSC: 65H10, 65J15, 49M15.
DOI: 10.4064/am2406-7-2020
Published online: 16 January 2021
Abstract
We study a nonlinear equation with a nondifferentiable part. The semi-local convergence of the Newton–Potra method is proved under weaker (than in earlier research) conditions on derivatives and divided differences of the first order. Weaker semi-local convergence criteria and tighter error estimations are obtained. Hence, the applicability of this method is extended too. These advantages are obtained under the same computational effort.
