Global dynamics of the real secant method

Identifier:  imarina:6170411

Handle: https://hdl.handle.net/20.500.11797/imarina6170411

Authors:  Garijo, Antonio; Jarque, Xavier

Abstract:
We investigate the root finding algorithm given by the secant method applied to a real polynomial p as a discrete dynamical system defined on R-2. We study the shape and distribution of the basins of attraction associated to the roots of p, and we also show the existence of other stable dynamics that might affect the efficiency of the algorithm. Finally we extend the secant map to the punctured torus T-infinity(2) which allow us to better understand the dynamics of the secant method near infinity and facilitate the use of the secant map as a method to find all roots of a polynomial.