6 papers
Application of polynomial algebras to non-linear equation solvers
Jordi Canela, Daniel Pérez-Palau
This paper presents a novel application of Jet Transport, a high-order automatic differentiation technique, to enhance classical numerical methods, with a focus on Newton's method.…
Boundedness and simple connectivity of the basins of attraction for some numerical methods
Jordi Canela, Antonio Garijo, Xavier Jarque
In this paper we study the dynamics of Halley's and Traub's root-finding algorithms applied to a symmetric family of polynomials of degree . We discuss the (un)boundedne…
Connected McMullen-like Julia sets in a Chebyshev-Halley Family
Jordi Canela, Antonio Garijo, Pascale Roesch
In this paper we study a one parameter family of rational maps obtained by applying the Chebyshev-Halley root finding algorithms. We show that the dynamics near parameters where th…
Dynamics of a Family of Rational Operators of Arbitrary Degree
Beatriz Campos, Jordi Canela, Antonio Garijo +1
In this paper we analyse the dynamics of a family of rational operators coming from a fourth-order family of root-finding algorithms. We first show that it may be convenient to red…
Dynamics of Newton-like root finding methods
Beatriz Campos, Jordi Canela, Pura Vindel
When exploring the literature, it can be observed that the operator obtained when applying \textit{Newton-like} root finding algorithms to the quadratic polynomials has the…
On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub
Jordi Canela, Vasiliki Evdoridou, Antonio Garijo +1
In this paper we study the dynamics of damped Traub's methods when applied to polynomials. The family of damped Traub's methods consists of root finding algorithms which con…