A note on the convergence of the irrational Halley’s iterative algorithm for solving nonlinear equations

Abstract

In this note a sufficient condition for the convergence of the irrational Halley’s formula for solving nonlinear equations is obtained. In addition, we propose a new proof for the third-order convergence that justifies the use of the plus sign in the algorithm.

KEYWORDS:

• Nonlinear functions
• iterative algorithms
• irrational Halley’s algorithm
• third-order convergence
• sufficient condition

2010 AMS SUBJECT CLASSIFICATIONS:

• 65H05
• 65H04

Acknowledgements

This work is dedicated to Dr Cleofé Campos-Pozuelo.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the National Agency for Research (AEI), Ministry of Science, Innovation, and Universities of Spain (Agencia Estatal de Investigación, Ministerio de Ciencia, Innovación y Universidades) and the European Regional Development Fund (FEDER) [grant number DPI2017-84758-P].