Given a set of values at , find the best
estimate of at .
Typically do by assuming is a polynomial---maybe of
degree 3 in this example.
Note that interpolation, like many optimization problems, is
mathematically undefined. One can find polynomials of degree 4 taking
any given values of , , , , and . We
can only determine value at by
polynomial of degree 3 (or other limiting assumption).
at 
, find the best
estimate of 
at 
.
is a polynomial---maybe of
degree 3 in this example.
, 
, 
, 
, and 
. We
can only determine value at 
by 
polynomial of degree 3 (or other limiting assumption).