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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/177922
Quadratures de Txebixov a l’interval i Teorema de Bernstein
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[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.
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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Jordi Marzo Sánchez
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OLIVER SANTACREU, Júlia. Quadratures de Txebixov a l’interval i Teorema de Bernstein. [consulted: 17 of June of 2026]. Available at: https://hdl.handle.net/2445/177922