On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub

Canela, Jordi; Evdoridou, Vasiliki; Garijo, Antonio and Jarque, Xavier (2023). On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub. Mathematische Zeitschrift, 303(3), article no. 55.

DOI: https://doi.org/10.1007/s00209-023-03215-8

Abstract

In this paper we study the dynamics of damped Traub’s methods T_δ when applied to polynomials. The family of damped Traub’s methods consists of root finding algorithms which contain both Newton’s (δ=0) and Traub’s method (δ=1). Our goal is to obtain several topological properties of the basins of attraction of the roots of a polynomial p under T₁, which are used to determine a (universal) set of initial conditions for which convergence to all roots of p can be guaranteed. We also numerically explore the global properties of the dynamical plane for T_δ to better understand the connection between Newton’s method and Traub’s method.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI

About

• Item ORO ID
• 87360
• Item Type
• Journal Item
• ISSN
• 1432-1823
• Extra Information
• Correction DOI - the original article has already been correct https://doi.org/10.1007/s00209-023-03232-7
• Keywords
• Holomorphic dynamics; Julia and Fatou sets; Basins of attraction; Root finding algorithms; Simple connectivity; Unboundedness
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2023 Springer Nature Switzerland AG
• Related URLs
• • https://doi.org/10.1007/s00209-023-03232...(Other)
• SWORD Depositor
• Jisc Publications-Router
• Depositing User
• Jisc Publications-Router