Jarque i Ribera, XavierRosado Rodríguez, David2023-04-122023-04-122022-06-12https://hdl.handle.net/2445/196609Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Xavier Jarque i Ribera[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.51 p.application/pdfcatcc-by-nc-nd (c) David Rosado Rodrı́guez, 2022http://creativecommons.org/licenses/by-nc-nd/3.0/es/Teoria geomètrica de funcionsTreballs de fi de grauEquacions funcionalsFuncions de variables complexesSistemes dinàmics complexosGeometric function theoryBachelor's thesesFunctional equationsFunctions of complex variablesComplex dynamical systemsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess