Quadrature rules and distribution of points on manifolds

2010/12/24 by Luca Brandolini, Christine Choirat, Brandolini, Luca +9
Mathematics · #42C15 #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Number Theory (math.NT) #Primary 41A55 #Secondary 11K38

paper · pdf · doi:10.48550/arxiv.1012.5409

openalex publication_date 2010/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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