We study the error in quadrature rules on a compact manifold. Our estimates are in the same spirit of the Koksma-Hlawka inequality and they depend on a sort of discrepancy of the sampling points and a generalized variation of the function. In particular, we give sharp quantitative estimates for quadrature rules of functions in Sobolev classes.

Brandolini, L., Choirat, C., Colzani, L., Gigante, G., Seri, R., Travaglini, G. (2014). Quadrature rules and distribution of points on manifolds. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, XIII(4), 889-923.

Quadrature rules and distribution of points on manifolds

COLZANI, LEONARDO;TRAVAGLINI, GIANCARLO
2014

Abstract

We study the error in quadrature rules on a compact manifold. Our estimates are in the same spirit of the Koksma-Hlawka inequality and they depend on a sort of discrepancy of the sampling points and a generalized variation of the function. In particular, we give sharp quantitative estimates for quadrature rules of functions in Sobolev classes.
Articolo in rivista - Articolo scientifico
quadrature rules, Koksma-Hlawka inequality, discrepancy
English
2014
XIII
4
889
923
none
Brandolini, L., Choirat, C., Colzani, L., Gigante, G., Seri, R., Travaglini, G. (2014). Quadrature rules and distribution of points on manifolds. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, XIII(4), 889-923.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/57963
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