A radial function centered at 
is a function 
of the form
 |
where the radial profile 
is a univariate
function and 
denotes the standard l2-norm. Thus
depends only on the distance
from 
to the center 
. For a discrete set of centers 
, one obtains a collection of translated radial
functions 
.
If these functions are linearly independent and span a vector
space 
,
they form a radial vector basis of 
and are known as radial
basis functions. Radial vector bases and radial
basis functions play an important role in many areas of mathematics and approximation
theory, including statistics and partial
differential equations.
