Abstract
Let X be a compact subset of the n-dimensional Euclidean space R n. A theorem of G. Björck implies the existence of a unique probability measure μ0 which maximizes the value ∫ X ∫ X d 2(x, y) dμ(x) dμ(y), where μ ranges over all probability measures on X and d 2 denotes the Euclidean distance on R n. In this paper we introduce and investigate an algorithm which is easy to describe and which inductively constructs a sequence ω = x 1, x 2,... in X such that ω is uniformly distributed with respect to μ0. Geometrical and topological interpretations and applications, and concrete numerical examples are given.
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Larcher, G., Schmid, W.C. & Wolf, R. On the Approximation of Certain Mass Distributions Appearing in Distance Geometry. Acta Mathematica Hungarica 87, 295–316 (2000). https://doi.org/10.1023/A:1006773702255
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DOI: https://doi.org/10.1023/A:1006773702255