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.
