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… 

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References

SHOWING 1-10 OF 13 REFERENCES
On Certain Configurations of Points in W” Which Are Unisolvent for Polynomial interpolation
We will denote the space of polynomials in n real variables by 2. .yj c .Y will bc those of total dcgrce at most d. Now suppose that E c R” is some set. Let I(E) := {p E 9’1 p is identically zero on
Fekete Potentials and Polynomials for Continua
TLDR
This work makes use of precise results of Pommerenke on the growth of the discriminant and on the distribution of the Fekete points, including the exterior Green function with pole at infinity.
On the Convergence of Optimal Measures
Using recent results of Berman and Boucksom (arXiv:0807.0035), we show that for a nonpluripolar compact set K⊂ℂd and an admissible weight function w=e−φ, any sequence of optimal measures converges
The Equivalence of Two Extremum Problems
Let f1 , …, fk be linearly independent real functions on a space X, such that the range R of (f1, …, fk) is a compact set in k dimensional Euclidean space. (This will happen, for example, if the fi
The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis
Canonical Moments. Orthogonal Polynomials. Continued Fractions and the Stieltjes Transform. Special Sequences of Canonical Moments. Canonical Moments and Optimal DesignFirst Applications.
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