Optimal Centers’ Allocation in Smoothing or Interpolating with Radial Basis Functions

Pedro González-Rodelas, Hasan M. H. Idais, Mohammed Yasin and Miguel Pasadas
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Pedro González-Rodelas: Departamento Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
Hasan M. H. Idais: Department of Mathematics and Statistics, Arab American University, Jenin P240, Palestine
Mohammed Yasin: Department of Mathematics, An-Najah National University, Nablus P400, Palestine
Miguel Pasadas: Departamento Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain

Mathematics, 2021, vol. 10, issue 1, 1-14

Abstract: Function interpolation and approximation are classical problems of vital importance in many science/engineering areas and communities. In this paper, we propose a powerful methodology for the optimal placement of centers, when approximating or interpolating a curve or surface to a data set, using a base of functions of radial type. In fact, we chose a radial basis function under tension (RBFT), depending on a positive parameter, that also provides a convenient way to control the behavior of the corresponding interpolation or approximation method. We, therefore, propose a new technique, based on multi-objective genetic algorithms, to optimize both the number of centers of the base of radial functions and their optimal placement. To achieve this goal, we use a methodology based on an appropriate modification of a non-dominated genetic classification algorithm (of type NSGA-II). In our approach, the additional goal of maintaining the number of centers as small as possible was also taken into consideration. The good behavior and efficiency of the algorithm presented were tested using different experimental results, at least for functions of one independent variable.

Keywords: approximation; interpolation; RBFs; centers’ allocation; MOGA; NSGA-II algorithms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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