On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub
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Otros documentos de la autoría: Canela, Jordi; Evdoridou, Vasiliki; Garijo, Antonio; Jarque, Xavier
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Mostrar el registro completo del ítemcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to TraubFecha de publicación
2023Editor
SpringerCita bibliográfica
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.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://link.springer.com/article/10.1007/s00209-023-03215-8Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
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. [-]
Publicado en
Mathematische Zeitschrift, 303, 55 (2023)Entidad financiadora
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
Código del proyecto o subvención
PID2020-118281GB-C32 | PID2020-118281GB-C33 | EP/R010560/1
Derechos de acceso
© The Author(s) 2023, corrected publication 2023
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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