Equidistribution of Fekete Points on the Sphere
نویسندگان
چکیده
منابع مشابه
Equidistribution of Fekete Points on the Sphere
Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of Fekete points in the sphere. The way we proceed is by showing their connection to other arrays of points, the so-called Marcinkiewicz-...
متن کاملEquidistribution of the Fekete Points on the Sphere
The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Z...
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A concept of generalized discrepancy, which involves pseudodiierential operators to give a criterion of equidistributed pointsets, is developed on the sphere. A simply structured formula in terms of elementary functions is established for the computation of the generalized discrepancy. With the help of this formula ve kinds of point systems on the sphere, namely lattices in polar coordinates, t...
متن کاملFekete Points
In this communication we present a new method to estimate Fekete points on surfaces. Our method works in a general setting, in the sense that we can obtain good estimations of the Fekete points on piecewise regular surfaces. The determination of Fekete points in the unit sphere is considered as a model of a highly non-linear optimization problem with non-linear constraints. In fact, obtaining a...
متن کاملOn the Spacing of Fekete Points for a Sphere, Ball or Simplex
Suppose that K ⊂ IR is either the unit ball, the unit sphere or the standard simplex. We show that there are constants c1, c2 > 0 such that for a set of Fekete points (maximizing the Vandermonde determinant) of degree n, Fn ⊂ K, c1 n ≤ min b∈Fn b 6=a dist(a, b) ≤ c2 n , ∀a ∈ Fn where dist(a, b) is a natural distance on K that will be described in the text. §
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ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2009
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-009-9051-5