Quasi-uniform designs with optimal and near-optimal uniformity constant

Luc Pronzato (1, 2) , Anatoly Zhigljavsky (3)

1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SYSTEMES
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 School of Mathematics [Cardiff]

A design is a collection of distinct points in a given set X, which is assumed to be a compact subset of R^d , and the mesh-ratio of a design is the ratio of its fill distance to its separation radius. The uniformity constant of a sequence of nested designs is the smallest upper bound for the mesh-ratios of the designs. We derive a lower bound on this uniformity constant and show that a simple greedy construction achieves this lower bound. We then extend this scheme to allow more flexibility in the design construction.

Domaines: Statistiques [math.ST]

Luc Pronzato, Anatoly Zhigljavsky. Quasi-uniform designs with optimal and near-optimal uniformity constant. Journal of Approximation Theory, In press. ⟨hal-03494864v2⟩