I am studying the Runge's phenomenon and there are a couple things I would like to understand better.
Suppose we interpolate the Runge's function with use equally spaced nodes to interpolate the function on the interval $[-1,1]$.
From what I understand the main reason the interpolation error grows with more nodes is because the value of $f^{n+1}(\xi)$ (where $f$ is the Runge function) grows really fast with $n$. Also, I believe that the reason because the error is higher in the extremes of the interval $[-1,1]$ is because of $w(x)=\prod_{i=0}^{n}(x-x_i)$.
Is this correct?
Furthermore, why do Chebyshev nodes interpolate the Runge function way better?