Quadrature rules and distribution of points on manifolds

Details Quadrature rules and distribution of points on manifolds Quadrature rules and distribution of points on manifolds

2010-12-24

arxiv.org/abs/1012.5409v1

Mathematics

Number Theory

Scientific paper

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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