Space-filling in high-dimensional sets

Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2025. Space-filling in high-dimensional sets. Presented at: International Conference of Numerical Analysis and Applied Mathematics:ICNAAM2023, Heraklion, Greece, 11-17 September 2023. AIP Conference Proceedings. , vol.3347 AIP Publishing, 10.1063/5.0286402

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Abstract

In this presentation, we discuss efficient construction of space-filling sets of points in high-dimensional sets X ⊂ ℝd. We show, in particular, that the usually recommended space-exploration schemes, formally optimal in the asymptotic considerations, are inefficient in the non-asymptotic regime. In particular, uniform sampling on entire X is much less efficient than uniform sampling on a suitable subset of X. The constructions proposed could be used in mesh-free approximation methods as well as in global optimization for devising efficient exploration strategies. The results discussed are based on the joint work of the author with Luc Pronzato (Sophia Antipolis, France) and Jack Noonan (Cardiff, UK).

Item Type:	Conference or Workshop Item (Paper)
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Publisher:	AIP Publishing
ISBN:	9780735452459
Last Modified:	19 Dec 2025 11:45
URI:	https://orca.cardiff.ac.uk/id/eprint/183380

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