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arxiv: 1012.5409 · v1 · pith:HA4U6KGUnew · submitted 2010-12-24 · 🧮 math.NT

Quadrature rules and distribution of points on manifolds

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keywords quadraturerulespointsclassescompactconsiderdiscrepancydistribution
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We study the error in quadrature rules on a compact manifold. As in the Koksma-Hlawka inequality, we consider a 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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