On the basins of attraction of root-finding algorithms

Authors

  • David Rosado Rodríguez

Keywords:

dynamical systems, root-finding algorithms, Newton’s method, Traub’s method.

Abstract

Els algoritmes de cerca d’arrels han estat històricament utilitzats per resoldre numèricament equacions no lineals de la forma f(x) = 0. Aquest treball explora la dinàmica dels mètodes de la família Traub parametritzada Tp,δ aplicada a polinomis. Aquests mètodes inclouen un ventall des del mètode de Newton (δ = 0) fins al mètode de Traub (δ = 1). El nostre enfocament rau a investigar diverses propietats topològiques de les conques d’atracció, particularment la seva simple connectivitat i la no acotació, que són crucials per identificar un conjunt universal de condicions inicials que assegurin la convergència a totes les arrels de p.

Downloads

Download data is not yet available.

Downloads

How to Cite

Rosado Rodríguez, D. (2024). On the basins of attraction of root-finding algorithms. Reports@SCM, 9(1), 103–104. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/154351

Issue

Vol. 9 No. 1 (2024)

Section

Extended abstracts

License

The intellectual property of articles belongs to the respective authors.
On submitting articles for publication to the journal Reports@SCM, authors accept the following terms:
  1. Authors assign to Societat Catalana de Matemàtiques (a subsidiary of Institut d’Estudis Catalans) the rights of reproduction, communication to the public and distribution of the articles submitted for publication to Reports@SCM.
  2. Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.
  3. Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.
  4. Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.
  5. The contents published in the journal, unless otherwise stated in the text or in the graphic material, are subject to a Creative Commons Attribution-NonCommercial-NoDerivs (by-nc-nd) 3.0 Spain licence, the complete text of which may be found at https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.en. Consequently, the general public is authorised to reproduce, distribute and communicate the work, provided that its authorship and the body publishing it are acknowledged, and that no commercial use and no derivative works are made of it.
  6. The journal Reports@SCM is not responsible for the ideas and opinions expressed by the authors of the published articles.