Polynomial interpolation is a way to find a smooth curve (polynomial) passing through a given set of data points.

For n given points we need a n-1 degree polynomial to model the behaviour.

Solving problems:

When given data points, plug it into the general equation for an n-1 degree polynomial and set up a system of equations. Solve the system using linear algebra or by using finite differences method.

General Interpolation equation

Where h is the distance between each x value