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arXiv · 2302.01001

QMC strength for some random configurations on the sphere

Víctor De La Torre·Jordi Marzo
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Abstract

A sequence $(X_N ) \subset \mathbb S^d$ 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 $\mathbb S^2$ based on numerical results. We study the average QMC strength for some related random configurations.

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Víctor De La Torre, Jordi Marzo. 2023-02-02. QMC strength for some random configurations on the sphere. https://arxiv.org/abs/2302.01001

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