MQ-Radial Basis Functions Center Nodes Selection with PROMETHEE Technique

In this paper‎, ‎we decide to select the best center nodes‎ ‎of radial basis functions by applying the Multiple Criteria Decision‎ ‎Making (MCDM) techniques‎. ‎Two methods based on radial basis‎ ‎functions to approximate the solution of partial differential‎ ‎equation by using collocation method are applied‎. ‎The first is based‎ ‎on the Kansa's approach‎, ‎and the second is based on the Hermite‎ ‎interpolation‎. ‎In addition‎, ‎by choosing five sets of center nodes‎: ‎Uniform grid‎, ‎Cartesian‎, ‎Chebyshev‎, ‎Legendre and‎ ‎Legendre-Gauss-Lobato (LGL) as alternatives and achieving the error‎, ‎the condition number of interpolation matrix and memory time as‎ ‎criteria‎, ‎rating of cases with the help of PROMETHEE technique is‎ ‎obtained‎. ‎In the end‎, ‎the best center nodes and method is selected‎ ‎according to the rankings‎. ‎This ranking shows that Hermite‎ ‎interpolation by using non-uniform nodes as center nodes is more‎ ‎suitable than Kansa's approach with each center node.

Keywords:

Multiple Criteria Decision Making‎ , ‎Radial basis‎ ‎functions‎ , ‎PROMETHEE‎ , ‎Hermite interpolation‎ , ‎Optimal selecting