On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub
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On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to TraubData de publicació
2023Editor
SpringerCita bibliogràfica
CANELA, Jordi, et al. On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub. Mathematische Zeitschrift, 2023, vol. 303, no 3, p. 55.Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
https://link.springer.com/article/10.1007/s00209-023-03215-8Versió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
In this paper we study the dynamics of damped Traub’s methods Tδ 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 ... [+]
In this paper we study the dynamics of damped Traub’s methods Tδ 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 Tδ to better understand the connection between Newton’s method and
Traub’s method. [-]
Publicat a
Mathematische Zeitschrift, 303, 55 (2023)Entitat finançadora
Universitat Jaume I | CRUE-CSIC agreement with Springer Nature | Ministerio de Economía y Competitividad | BGSMath Banco de Santander Postdoctoral 2017 | London Mathematical Society | IMUB | EPSRC
Codi del projecte o subvenció
PID2020-118281GB-C32 | PID2020-118281GB-C33 | EP/R010560/1
Drets d'accés
© The Author(s) 2023, corrected publication 2023
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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