Interpolation

A type of estimation. A method of constructing new data points based on the range of a discrete set of known data points. It is the process of deriving a simple function from a set of discrete data points so that the function passes through all the given data points and can be used to estimate data points in-between the given ones.

Weierstrass Approximation Theorem

Suppose is continuous on . Then such that :

Note

For data points, there is one and only one polynomial of order that passes through all the points.