Space-filling in high-dimensional sets
Anatoly A. Zhigljavsky · AIP conference proceedings · 2025
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).