21 citations · 44 across the 12 of their papers we have counts for
16 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…
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 cont…
Computing parameter planes of iterative root-finding methods with several free critical points
Beatriz Campos, Jordi Canela, Alberto Rodríguez-Arenas +1
In this paper we present an algorithm to obtain the parameter planes of families of root-finding methods with several free critical points. The parameter planes show the joint beha…
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…
Dynamical mechanism behind ghosts unveiled in a map complexification
Jordi Canela, Lluís Alsedà, Núria Fagella +1
Complex systems such as ecosystems, electronic circuits, lasers or chemical reactions can be modelled by dynamical systems which typically experience bifurcations. Transients typic…
Achievable connectivities of Fatou components for a family of singular perturbations
Jordi Canela, Xavier Jarque, Dan Paraschiv
In this paper we study the connectivity of Fatou components for maps in a large family of singular perturbations. We prove that, for some parameters inside the family, the dynamica…
Tips of Tongues in the Double Standard Family
Kuntal Banerjee, Xavier Buff, Jordi Canela +1
We answer a question raised by Misiurewicz and Rodrigues concerning the family of degree 2 circle maps defined by \[F_λ(x) := 2…
Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials
Beatriz Campos, Jordi Canela, Purificación Vindel
We study the Chebyshev-Halley family of root finding algorithms from the point of view of holomorphic dynamics. Numerical experiments show that the speed of convergence to the root…
Julia sets with a wandering branching point
Xavier Buff, Jordi Canela, Pascale Roesch
According to the Thurston No Wandering Triangle Theorem, a branching point in a locally connected quadratic Julia set is either preperiodic or precritical. Blokh and Oversteegen pr…
Rational maps with Fatou components of arbitrarily large connectivity
Jordi Canela
We study the family of singular perturbations of Blaschke products . We analyse how the connectivity of the Fatou components…
Singular perturbations of Blaschke Products and connectivity of Fatou components
Jordi Canela
The goal of this paper is to study the family of singular perturbations of Blaschke products given by . We focus on the study…
Tongues in Degree 4 Blaschke Products
Jordi Canela, Núria Fagella, Antonio Garijo
The goal of this paper is to investigate the family of Blasche products , which is a rational family of perturbations of the doubling map. We focu…
On a Family of Rational Perturbations of the Doubling Map
Jordi Canela, Núria Fagella, Antonio Garijo
The goal of this paper is to investigate the parameter plane of a rational family of perturbations of the doubling map given by the Blaschke products $B_a(z)=z^3\frac{z-a}{1-\bar{a…