El mètode de Newton com a sistema dinàmic

Abstract

[en] Newton’s method, first introduced in 1669, is one of the most well-known root-finding algorithm. At the end of the nineteenth century, it emerged the idea of study the algorithm as a dynamical system in the complex plane, with the aim of understand the behavior of the method in a global way. The main goal of this thesis is to understand Newton’s method applied to polynomials as a rational function, studying properties and convergence results, as well as, showing an algorithm to find all roots of a complex polynomial through Newton’s method. We are also going to study the iterative system applied to a special case of entire function and we will give a possible innovation to find all roots of a complex plynomial with Newton’s method through this type of functions.