Fekete Points, Formation Control, and the Balancing Problem
نویسندگان
چکیده
منابع مشابه
Fekete 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...
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In this paper we present a procedure for the numerical estimation of the Fekete points of a wide variety of compact sets in IR. We understand the problem of the Fekete points in terms of the identification of nearly equilibrium configurations for a potential energy that depends on the relative position of N particles. The compact sets for which our procedure has been designed can be described b...
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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-...
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We compute approximate Fekete points for weighted polynomial interpolation by a recent algorithm based on QR factorizations of Vandermonde matrices. We consider in particular the case of univariate and bivariate functions with prescribed poles or other singularities, which are absorbed in the basis by a weight function. Moreover, we apply the method to the construction of real and complex weigh...
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ژورنال
عنوان ژورنال: IEEE Transactions on Automatic Control
سال: 2017
ISSN: 0018-9286,1558-2523
DOI: 10.1109/tac.2017.2679073