Estimation of Fekete points

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 basically as the finite union of piecewise regular surfaces and curves. To determine a good configuration to start the search of the Fekete points of these objects, we construct a sequence of approximating regular surfaces. Our algorithm is based in the concept of disequilibrium degree, defined from 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 compact set considered as well as of the kernel used to define the energy. The numerical experimentation suggests that a nearly optimal configuration can be obtained by means of the procedure introduced here with a total computational cost of order less than N3.