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/Tutor: | Jarque i Ribera, Xavier |
Keywords: | Funcions de variables complexes Sistemes dinàmics diferenciables Treballs de fi de màster Algorismes computacionals Varietats complexes Functions of complex variables Differentiable dynamical systems Master's 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 Oficial - Matemàtica Avançada |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
memoria.pdf | Memòria | 4.43 MB | Adobe PDF | View/Open |
This item is licensed under a
Creative Commons License