• DOI:10.48550/arXiv.2205.06498
• Corpus ID: 248798582

On Fekete Points for a Real Simplex

@article{Bos2022OnFP,
  title={On Fekete Points for a Real Simplex},
  author={Len P. Bos},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.06498}
}

• L. Bos
• Published 13 May 2022
• Mathematics
• ArXiv

We survey what is known about Fekete points/optimal designs for a simplex in R d . Several new results are included. The notion of Fejér exponenet for a set of interpolation points is introduced. In as is well known, the Chebyshev points provide an ex-cellent set of points for polynomial interpolation of functions defined on the interval , 1] . In several the problem of finding analogues of such near optimal interpolation points is much more difficult and each un-derlying set K ⊂ R d must be analyzed indvidually. One general approach, that turns out to be rather fruitful, is to consider the so-called Fekete points (see Definition 0.1 below). These turn out to be strongly related to statis-tical Optimal Designs (cf. Definition 0.3) and to a property proved first by Fejér [6] (cf. Defintion 0.2)in the interval case. In this work we survey what is known about Fekete points for the case of K ⊂ R d , a simplex. Some new results are obtained and we introduce the notion of Fejér exponent for a set of interpolation points. We remark that also in the univariate complex case, K ⊂ C , Fekete points and their properties have been much studied,