# On the Spacing of Fekete Points for a Sphere, Ball or Simplex

## Len Bos, Norm Levenberg and Shayne Waldron

## Abstract:

Suppose that $K\subset\RR^d$ is either the unit ball, the unit sphere
or the standard simplex. We show that there are constants $c_1,c_2>0$ such that
for a set of Fekete points (maximizing the Vandermonde determinant) of degree $n,$ $F_n\subset K,$
$${c_1\over n}\le \min_{b\in F_n\atop b\neq a} \hbox{dist}(a,b)\le {c_2\over n},\quad\forall a\in F_n$$
where $\hbox{dist}(a,b)$ is a natural distance on $K$ that
will be described in the text.

**Keywords:**
Fekete points

**Math Review Classification:**
Primary ;
Secondary

**Length:** 15 pages

**Last Updated:** 1 January 2008

## Availability: