Items for "spherical design"

On Euclidean designs

A Euclidean t-design, as introduced by Neumaier and Seidel (1988), is a finite set 𝒳 ⊂ ℝⁿ with a weight function w : 𝒳 → ℝ⁺ for which holds for every polynomial ƒ of total degree at most t; here R is the set of norms of the points in 𝒳, W_r is the total weight of all elements of 𝒳 with norm r, S_r is the n-dimensional sphere of radius r centered at the origin, and is the average of ƒ over S_r...

Keywords: Euclidean design, spherical design, interval design, GaussJacobi quadrature, Gegenbauer polynomial, tight design, harmonic polynomial