A radial function is a function satisfying for points in some subset . Here, denotes the standard Euclidean norm in and is a discrete subset of whose elements are called centers.
A collection of such functions which independently span a space is usually called a radial basis of . In this case, the functions are known as radial basis functions. Radial bases and radial basis functions play an important role in many areas of mathematics and approximation theory including statistics and partial differential equations.