Jarque i Ribera, XavierOlea Martínez, Javier2015-06-152015-06-152015-01-19https://hdl.handle.net/2445/65849Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2015, Director: Xavier Jarque i RiberaOne of the most classical problems in Mathematics is to find the zeroes of a given function $f$, or equivalently, to find the roots of the equation $f (z) = 0$. It has been studied this problem, from the simplest cases, like the case of $f$ being a polynomial of one or several real or complex variables, to a more general setting, like the case of $f$ being just a continuous function. Using algebraic and analytic methods it is possible to exactly solve the equation $f (x) = 0$ rarely. A part from these particular situations (like polynomials of degree less than 5) the unique approximation is to numerically find them; that is to construct root finding algorithms which allow us to find good approximations of the zeroes of $f$. The more well know root finding algorithms are defined by an iterative mechanism, and so, they can be thought and treated as dynamical systems defined in a certain space.58 p.application/pdfengcc-by-sa (c) Javier Olea Martínez, 2015http://creativecommons.org/licenses/by-sa/3.0/es/Funcions de variables complexesSistemes dinàmics diferenciablesTreballs de fi de màsterAlgorismes computacionalsVarietats complexesFunctions of complex variablesDifferentiable dynamical systemsMaster's thesesComputer algorithmsinfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess