Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/65849
Title: Root finding methods: a dynamical approach
Author: Olea Martínez, Javier
Director: Jarque i Ribera, Xavier
Keywords: Funcions de variables complexes
Sistemes dinàmics diferenciables
Tesis de màster
Algorismes computacionals
Varietats complexes
Functions of complex variables
Differentiable dynamical systems
Masters theses
Computer algorithms
Issue Date: 19-Jan-2015
Abstract: One 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.
Note: Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2015, Director: Xavier Jarque i Ribera
URI: http://hdl.handle.net/2445/65849
Appears in Collections:Màster - Matemàtica Avançada

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