Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/177922
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Marzo Sánchez, Jordi | - |
dc.contributor.author | Oliver Santacreu, Júlia | - |
dc.date.accessioned | 2021-06-03T09:15:33Z | - |
dc.date.available | 2021-06-03T09:15:33Z | - |
dc.date.issued | 2020-06-21 | - |
dc.identifier.uri | http://hdl.handle.net/2445/177922 | - |
dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Jordi Marzo Sánchez | ca |
dc.description.abstract | [en] In this work we will prove a theorem that Bernstein proved in 1937. This theorem states that there are no quadrature formulas with equal weights (of Chebyshev) in the interval $[-1,1]$ $$ \int_{-1}^{1} f(x) d x \approx \frac{2}{n} \sum_{k=1}^{n} f\left(x_{k}\right) $$ that are true for polynomials $f$ of degree $\leq n$, with nodes $x_{k} \in[-1,1]$, if $n \geq 10$. We will also see some results related to the distribution of these nodes when $n$ is large. | ca |
dc.format.extent | 39 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | cat | ca |
dc.rights | cc-by-nc-nd (c) Júlia Oliver Santacreu, 2020 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | - |
dc.subject.classification | Funcions hipergeomètriques | ca |
dc.subject.classification | Treballs de fi de grau | - |
dc.subject.classification | Polinomis ortogonals | ca |
dc.subject.classification | Teoria de l'aproximació | ca |
dc.subject.classification | Integració numèrica | ca |
dc.subject.other | Hypergeometric functions | en |
dc.subject.other | Bachelor's theses | - |
dc.subject.other | Orthogonal polynomials | en |
dc.subject.other | Approximation theory | en |
dc.subject.other | Numerical integration | en |
dc.title | Quadratures de Txebixov a l’interval i Teorema de Bernstein | ca |
dc.type | info:eu-repo/semantics/bachelorThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
177922.pdf | Memòria | 525.51 kB | Adobe PDF | View/Open |
This item is licensed under a
Creative Commons License