On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub
View/ Open
Impact
Scholar |
Other documents of the author: Canela, Jordi; Evdoridou, Vasiliki; Garijo, Antonio; Jarque, Xavier
Metadata
Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to TraubDate
2023Publisher
SpringerBibliographic citation
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.Type
info:eu-repo/semantics/articlePublisher version
https://link.springer.com/article/10.1007/s00209-023-03215-8Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
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. [-]
Is part of
Mathematische Zeitschrift, 303, 55 (2023)Funder Name
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
Project code
PID2020-118281GB-C32 | PID2020-118281GB-C33 | EP/R010560/1
Rights
© The Author(s) 2023, corrected publication 2023
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
This item appears in the folowing collection(s)
- IMAC_Articles [122]
- MAT_Articles [766]