5. Interpolation between Chebyshev points

We've seen that the interpolation polynomial between equidistant points is unusable, and that the best approximation suffers from flaws that are often prohibitive. So what's to be done? Later on, we'll take a look at some linear methods of interpolation between equidistant points, which may not be polynomial, but which nonetheless allow the "fundamental idea" to be properly realized.

For the moment, we're going to look at polynomial interpolation in the case where the nodes can be chosen. How can we proceed? One approach involves the $\mathcal{l}$ function of (4)...