21 citations · 44 across the 12 of their papers we have counts for
6 papers · 1 filter
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.…
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…
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…