On Fekete Points for a Real Simplex

TL;DR

This paper surveys the theory of Fekete points for simplexes in real space, introduces the Fejér exponent concept, and presents new results on optimal interpolation point distributions.

Contribution

It provides a comprehensive survey of Fekete points on simplexes and introduces the novel concept of Fejér exponent with new related results.

Findings

Introduction of Fejér exponent for interpolation points

New results on Fekete points for simplexes

Enhanced understanding of optimal designs in $\\R^d$

Abstract

We survey what is known about Fekete points/optimal designs for a simplex in $\R^d.$ Several new results are included. The notion of Fej\'er exponenet for a set of interpolation points is introduced.