Root finding techniques that work
Abstract
In most introductory numerical analysis textbooks, the treatment of a single nonlinear equation often consists of a collection of all-purpose methods that frequently do not work or are inefficient. These textbooks neglect to teach the importance of adapting a method to the given problem, and consequently also neglect to provide the tools to accomplish this. Several general techniques are described here to incorporate the specific structure or properties of a nonlinear equation into a method for solving it. This can mean the construction of a method specifically tailored to the equation, or the transformation of the equation into an equivalent one for which an existing method is well-suited. The techniques are illustrated with the help of several case studies taken from the literature.
Cite
@article{arxiv.2204.02326,
title = {Root finding techniques that work},
author = {Aaron Melman},
journal= {arXiv preprint arXiv:2204.02326},
year = {2022}
}
Comments
15 pages, 5 figures