3 papers
math.DS2020
Topological properties of the immediate basins of attraction for the secant method
Laura Gardini, Antonio Garijo, Xavier Jarque
We study the discrete dynamical system defined on a subset of given by the iterates of the secant method applied to a real polynomial . Each simple real root of ha…
math.DS2019
The secant map applied to a real polynomial with multiple roots
Antonio Garijo, Xavier Jarque
We investigate the plane dynamical system given by the secant map applied to a polynomial having at least one multiple root of multiplicity . We prove that the local dynam…
math.DS2018
Global dynamics of the real secant method
Antonio Garijo, Xavier Jarque
We investigate the root finding algorithm given by the secant method applied to a real polynomial as a discrete dynamical system defined on . We study the shape an…