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Journal Articles Journal of Approximation Theory Year : 2023

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

Abstract

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.
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Dates and versions

hal-03494864 , version 1 (20-12-2021)
hal-03494864 , version 2 (06-06-2023)

Identifiers

  • HAL Id : hal-03494864 , version 2

Cite

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