Quadrature rules and distribution of points on manifolds

By L. Brandolini, Christine Choirat, L. Colzani, G. Gigante, Raffaello Seri, G. Travaglini. 2010

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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.

Subfields: Algebra and Number Theory, Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e58525578d223af99a188262f61055c42a7b18d6