Polyharmonic spline

Summary

A polyharmonic spline is a sum of translates of one radial basis function $\varphi(\norm{x})$ on $\R^d$ plus a low degree polynomial. The radial function is $r^{2m-d}$ or $r^{2m-d} \log r$, a multiple of the fundamental solution of the iterated Laplacian $\Delta^m$ in $\R^d$. Polyharmonic splines solve scattered data interpolation with minimal "energy", and the thin plate spline is the best known case.