On the basins of attraction of root-finding algorithms Authors David Rosado Rodríguez Universitat de Barcelona Keywords: dynamical systems, root-finding algorithms, Newton’s method, Traub’s method Abstract Root-finding algorithms have historically been used to numerically solve nonlinear equations of the form f (x)=0. This paper studies the dynamics of the parameterized Traub family Tp,δ applied to polynomials, ranging from Newton’s method (δ = 0) to Traub’s method (δ = 1). We focus on topological properties of the immediate basins of attraction of the finite fixed points, especially simple connectivity and unboundedness, which are key to identifying a universal set of initial conditions ensuring convergence to all roots of p. Downloads Download data is not yet available. Downloads PDF Published 2025-12-04 How to Cite Rosado Rodríguez, D. (2025). On the basins of attraction of root-finding algorithms. Reports@SCM, 10(1), 13–21. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/154822 More Citation Formats ACM ACS APA ABNT Chicago Harvard IEEE MLA Turabian Vancouver Download Citation Endnote/Zotero/Mendeley (RIS) BibTeX Issue Vol. 10 No. 1 (2025) Section Articles 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: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.Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.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.The journal Reports@SCM is not responsible for the ideas and opinions expressed by the authors of the published articles.
