Thanks for writing this up. Seeing "cute" examples like this is actually helpful, because I don't need to learn a particular application area while reading about the solution method. It's a great way to get me started thinking about new ways of approaching old problems.

While you play around with the how the algorithm parameters affect its ability to find the polynomial coefficients, it would be nice to see how adding some random noise to the sample points affects it, as well. This would make your example more realistic (because it would mean you'll never be able to generate a perfect fit).