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

Pronzato, Luc and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2023. Quasi-uniform designs with optimal and near-optimal uniformity constant. Journal of Approximation Theory 294 , 105931. 10.1016/j.jat.2023.105931

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Abstract

A design is a collection of distinct points in a given set X , which is assumed to be a compact subset of Rd, 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0021-9045
Date of First Compliant Deposit:	21 June 2023
Date of Acceptance:	3 June 2023
Last Modified:	21 Jul 2023 03:10
URI:	https://orca.cardiff.ac.uk/id/eprint/160489

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