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DC Field | Value | Language |
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dc.contributor.advisor | Tatjer i Montaña, Joan Carles | - |
dc.contributor.author | Fernández Benítez, Daniel | - |
dc.date.accessioned | 2022-04-21T07:50:53Z | - |
dc.date.available | 2022-04-21T07:50:53Z | - |
dc.date.issued | 2021-06-20 | - |
dc.identifier.uri | http://hdl.handle.net/2445/185071 | - |
dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Joan Carles Tatjer i Montaña | ca |
dc.description.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. | ca |
dc.format.extent | 67 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | cat | ca |
dc.rights | cc-by-nc-nd (c) Daniel Fernández Benítez, 2021 | - |
dc.rights | codi: GPL (c) Daniel Fernández Benítez, 2021 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.rights.uri | http://www.gnu.org/licenses/gpl-3.0.ca.html | - |
dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | - |
dc.subject.classification | Anàlisi funcional | ca |
dc.subject.classification | Treballs de fi de grau | - |
dc.subject.classification | Espais de Banach | ca |
dc.subject.classification | Mètode de Newton-Raphson | ca |
dc.subject.classification | Operadors no lineals | ca |
dc.subject.other | Functional analysis | en |
dc.subject.other | Bachelor's theses | - |
dc.subject.other | Banach spaces | en |
dc.subject.other | Newton-Raphson method | en |
dc.subject.other | Nonlinear operators | en |
dc.title | Mètode de Newton en espais de Banach: teorema de Kantorovich i aplicacions | ca |
dc.type | info:eu-repo/semantics/bachelorThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
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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