QMC Strength for Some Random Configurations on the Sphere

被引：0
|
作者：
de la Torre, Victor [1 ]
Marzo, Jordi [1 ,2 ]
机构：
[1] Univ Barcelona, Dept Matemat & Informat, Gran Via 585, Barcelona 08007, Spain
[2] Ctr Recerca Matemat, Edifici C,Campus Bellaterra, Bellaterra 08193, Spain
来源：
MONTE CARLO AND QUASI-MONTE CARLO METHODS, MCQMC 2022 | 2024年 / 460卷
关键词：
Random point processes; QMC design; Sphere; Discrepancy; Discrete energy; INTEGRATION; POINTS;
D O I：
10.1007/978-3-031-59762-6_31
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A sequence (X-N) subset of 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 sgreaterthanSuperscriptasteriskBaselineperiod s > s*. In [15] conjectured values of the strength are given for some well known point families S-2 based on numerical results. We study the average QMC strength for some related random configurations.
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页码：625 / 642
页数：18
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