Radial Basis Function - Approximation

Approximation

Radial basis functions are typically used to build up function approximations of the form

where the approximating function y(x) is represented as a sum of N radial basis functions, each associated with a different center x_i, and weighted by an appropriate coefficient w_i. The weights w_i can be estimated using the matrix methods of linear least squares, because the approximating function is linear in the weights.

Approximation schemes of this kind have been particularly used in time series prediction and control of nonlinear systems exhibiting sufficiently simple chaotic behaviour, 3D reconstruction in computer graphics (for example, hierarchical RBF and Pose Space Deformation).