Polynomial Interpolation using large set of data.

Question

I have a large set of {$x_i$}$_{i=1}^n$ and corresponding values of the function {$f(x_i)$}$_{i=1}^n$. My aim is to estimate the function $f(x)$. Therefore, I think that appropriate technique is Lagrange Polynomial Interpolation. The problem is: as I mentioned I have large set of observations (e.g. 100), then using Lagrange Polynomial Interpolation we will find a $n-1$ degree polynomial, which is meaningless to write explicitly. Please guide me in order to pick up the correct technique or use some modification (if any) to estimate the function, which could be written explicitly.