Radial basis function interpolation

Summary

Radial basis function interpolation fits scattered data in $\R^d$ with a combination of translates of one radial basis function. There is one translate centred at each data point. The coefficients solve a square linear system whose matrix collects the values of the radial function at all pairwise distances. For many radial functions, such as the Gaussian and the inverse multiquadric, this matrix is invertible for every set of distinct points in every dimension. This makes it one of the main methods of multivariate interpolation, free of the restrictions on point position that polynomial interpolation has.