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*). In general this is done by developing a smooth curve though the points (x1, f(x1)), (x2, f(x2)), ... (xN, f(xN)).
Interpolation is a basic numerical method and the subject is generally covered in books on numerical methods or numerical analysis. Numerical methods for carrying out interpolation can be found in numerical libraries.
Numerical Libraries
There are two widely-used general libraries
on numerical methods:
NAG (Numerical Algorithms Group) and
IMSL
(International Mathematics and Statistical Library).
www.science-books.net