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.
Titolo: | Quadrature rules and distribution of points on manifolds | |
Tutti gli autori: | Brandolini, Luca; Choirat, Christine; Colzani, Leonardo; Gigante, Giacomo; Seri, Raffaello; Travaglini, Giancarlo | |
Data di pubblicazione: | 2013 | |
Abstract (eng): | 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. | |
Nelle collezioni: | Working papers ENG. Mathematics and Statistics Series (2013- ) |
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