We may know the value of a function f at a set of points
x1, x2, ..., xN. How do we estimate the value of the function
at any point x*; how do we compute f(x*). This
can be achieved by finding a smooth curve that passes though the
points (x1, f(x1)), (x2, f(x2)), ... (xN, f(xN)). Alternatively,
the points may be joined in sebintervals of [x1,xN] by
piecewise . A third method is that of defining a
straight line (or a polynomial of low degree) that is the best fit to the
set of points.
Methods for interpolation are basic numerical methods and the
subject is generally covered in books on
numerical methods.