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.
Quadrature rules and distribution of points on manifolds
BRANDOLINI, Luca;GIGANTE, Giacomo;
2013-01-01
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.File allegato/i alla scheda:
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