Functional networks and the lagrange polynomial interpolation

Abstract

A new approach is presented for the approximation of a scalar function defined on a discrete set of points. The method is based on the application of functional networks and the Lagrange interpolation formula. The interpolation mechanism of the separable functional networks when the neuron functions are approximated by Lagrange polynomials, is explored. The coefficients of the Lagrange interpolation formula are estimated during the learning of the functional network by simply solving a linear system of equations. Finally, several examples show the effectiveness of the proposed interpolation method. © Springer-Verlag Berlin Heidelberg 2006.