# Interpolation

Given a set of data points. Estimation of the unknown quantity inside the data set with the help of a polynomial is termed as interpolation. This is the mathematical definition of interpolation.

An easier way to imagine this is by considering a case where you know the value of output at different input values. Now you wish to find out the value at a point which lies between that data set but whose value is unknown.

You will use interpolation to get a polynomial of order n if the number of known points is n+1. Now, put any input value between the data set and you’ll get the output.

The numerical analysis provides you with multiple methods for interpolation, some of them being LaGrange’s interpolation, Newton divided difference, newton’s forwards and backward difference and Neville interpolation. Where each of these methods has its special usage areas.

One popular application of interpolation is in the heat transfer equation. Consider a metal bar of uniform length which is being heated from one side and the other side is connected to a cold reservoir.