Estimation of Fekete points
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In this paper we present a new method to estimate Fekete points on surfaces. Although our method works in a general setting, we concentrate on its application to the unit sphere because it is the prototype problem and in the unit cube because its singularity. The algorithm we present here is very simple and it is based in a physical interpretation of the behavior of a system of particles when they search for a minimal energy configuration. Moreover, the algorithm is efficient and robust independently of the surface and the kernel used to define the energy. The algorithm allows us to work with a great number of particles, for instance, in less than a day of calculation time, we have obtained a good configuration for 50000 particles in the unit sphere without using symmetry properties and with a conventional PC.