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Integration of polynomials

Paweł Szeptycki (2004)

Applicationes Mathematicae

We prove that the only functions for which certain standard numerical integration formulas are exact are polynomials.

Interpolants d'Hermite C2 obtenus par subdivision

Jean-Louis Merrien (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a two point subdivision scheme with parameters to draw curves that satisfy Hermite conditions at both ends of [a,b]. We build three functions f,p and s on dyadic numbers and, using infinite products of matrices, we prove that, under assumptions on the parameters, these functions can be extended by continuity on [a,b], with f'=p and f''=s .

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