A novel Newton-Raphson style root finding algorithm
Numerical Analysis
2023-09-06 v1 Numerical Analysis
Abstract
Many problems in applied mathematics require root finding algorithms. Unfortunately, root finding methods have limitations. Firstly, regarding the convergence, there is a trade-off between the size of it's domain and it's rate. Secondly the numerous evaluations of the function and its derivatives penalize the efficiency of high order methods. In this article, we present a family of high order methods, that require few functional evaluations ( One for each step plus one for each considered derivative at the start of the method), thus increasing the efficiency of the methods.
Cite
@article{arxiv.2309.00698,
title = {A novel Newton-Raphson style root finding algorithm},
author = {Komi Agbalenyo and Vincent Cailliez and Jonathan Cailliez},
journal= {arXiv preprint arXiv:2309.00698},
year = {2023}
}
Comments
11 pages, 3 tables, submited to Applied Mathematics and Computation