Package smile.math.rbf
Sums of radial basis functions are typically used to approximate given functions:
y(x) = Σ w_{i} φ(xc_{i})
where the approximating function y(x) is represented as a sum of N radial basis functions, each associated with a different center c_{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.
This approximation process can also be interpreted as a simple kind of neural network and has been particularly used in time series prediction and control of nonlinear systems exhibiting sufficiently simple chaotic behavior, 3D reconstruction in computer graphics (for example, hierarchical RBF).

ClassDescriptionGaussian RBF.Inverse multiquadric RBF.Multiquadric RBF.A radial basis function (RBF) is a realvalued function whose value depends only on the distance from the origin, so that φ(x)=φ(x); or alternatively on the distance from some other point c, called a center, so that φ(x,c)=φ(xc).Thin plate RBF.