Many sciences and other areas of research and applications
from engineering to economics require the approximation
of functions that depend on many variables.
This can be for a variety of reasons. Sometimes
we have a discrete set of data points and we
want to find an approximating function that completes
this data; another possibility is that precise
functions are either not known or it would take too
long to compute them explicitly. In this snapshot
we want to introduce a particular method of approximation
which uses functions called radial basis functions.
This method is particularly useful when approximating
functions that depend on very many variables.
We describe the basic approach to approximation
with radial basis functions, including their computation,
give several examples of such functions and
show some applications.