Extended convergence analysis of the Newton–Potra method under weak conditions

Ioannis K. Argyros, Stepan Shakhno, Yuriy Shunkin, Halyna Yarmola Applicationes Mathematicae 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.

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