QMC strength for some random configurations on the sphere

2023/02/02 by Víctor De La Torre, De La Torre, Víctor, Jordi Marzo +1
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2302.01001

openalex publication_date 2023/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A sequence (X_N ) ⊂ \mathbb S^d of N-point sets from the d-dimensional sphere has QMC strength s^*>d/2 if it has worst-case error of optimal order, N^s/d, for Sobolev spaces of order s for all d/2 < s < s^* , and the order is not optimal for s > s^* . In arXiv:1208.3267 conjectured values of the strength are given for some well known point families in \mathbb S² based on numerical results. We study the average QMC strength for some related random configurations.

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