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Title: | Mètode de Newton en espais de Banach: teorema de Kantorovich i aplicacions |
Author: | Fernández Benítez, Daniel |
Director/Tutor: | Tatjer i Montaña, Joan Carles |
Keywords: | Anàlisi funcional Treballs de fi de grau Espais de Banach Mètode de Newton-Raphson Operadors no lineals Functional analysis Bachelor's theses Banach spaces Newton-Raphson method Nonlinear operators |
Issue Date: | 20-Jun-2021 |
Abstract: | [en] Let the equation $F x=\overrightarrow{0}$, where $F: X \mapsto Y, X$ and $Y$ are Banach spaces of like dimension, Kantorovich's Theorem gives sufficient conditions for the equation to have a solution $x^{*}$, locally unique, close to a previously picked $x^{0} \in X$, and that the Newton's method with initial condition $x^{0}$ converges to it. Moreover, gives sharp estimations of the regions where $x^{*}$ exists and is unique. In this thesis we state Kantorovich's Theorem and prove it in two different ways: by recurrence and by majorant sequences. Besides, some variants and like results are stated, along with applications and examples on how to make use of the Theorem. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Joan Carles Tatjer i Montaña |
URI: | http://hdl.handle.net/2445/185071 |
Appears in Collections: | Programari - Treballs de l'alumnat Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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TFG-codi-font.tar | Codi font | 58.5 kB | Unknown | View/Open |
tfg_daniel_fernandez_benitez.pdf | Memòria | 741.06 kB | Adobe PDF | View/Open |
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