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, 13(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.
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