WIT Press


DETERMINATION OF SHAPE PARAMETER IN RBF APPROXIMATION

Price

Free (open access)

Paper DOI

10.2495/BE410141

Volume

122

Pages

10

Page Range

153 - 162

Published

2019

Author(s)

ANDREAS KARAGEORGHIS, PINELOPI TRYFONOS

Abstract

We apply a radial basis function (RBF) collocation method for the approximation of functions in two dimensions. The solution is approximated by a linear combination of radial basis functions. The issue of determining the optimal value of the shape parameter is tackled by including it in the unknowns along with the coefficients of the RBFs in the approximation. The resulting nonlinear system of equations is solved by directly applying a standard non-linear solver. The results of some numerical experiments are presented and analysed.

Keywords

radial basis functions, function approximation, collocation