Computational cost of the Fekete problem I: The Forces Method on the 2-sphere

Authors:
E. Bendito;A. Carmona;A. M. Encinas;J. M. Gesto;A. Gómez;C. Mouriño;M. T. Sánchez
Affiliations:
Departament de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain;Departament de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain;Departament de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain;Departament de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain;Fundación Centro Tecnológico de Supercomputación de Galicia, CESGA, Santiago de Compostela, Spain;Fundación Centro Tecnológico de Supercomputación de Galicia, CESGA, Santiago de Compostela, Spain;Fundación Centro Tecnológico de Supercomputación de Galicia, CESGA, Santiago de Compostela, Spain
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

Here, we study the computational complexity of the Fekete point problem. Namely, we give an exhaustive description of the main properties of an algorithm for the minimization of the logarithmic potential energy on the 2-sphere, and we characterize the probability distribution of the cost of the different minima. In particular, we show that a local minimum can be found with an average cost of about O(N^2^.^8).