Radial basis function

Summary

A radial basis function is a function on $\R^d$ whose value depends only on the distance from a centre point. Standard examples are the Gaussian $e^{-(\varepsilon r)^2}$, the multiquadric $\sqrt{1 + (\varepsilon r)^2}$ and the thin plate spline $r^2 \log r$, where $r$ is the distance. Shifted copies centred at data points are used as building blocks for radial basis function interpolation of scattered data in any dimension. They also appear as kernels in machine learning and in meshfree methods for differential equations.