Great post! The author touches on Chebychev polynomials, which are the basis for quite a few numerical analysis tricks, including conjugate gradient [1], accelerated gradient descent [2], and Chebychev semi-iterative methods (which find the best combination of past iterates to use during an optimization procedure; sadly I can't find a good reference).
There are a number of facts/folklore about Chebychev polynomials that seem to go stated without proof in a lot of papers, so a few years ago I wrote up some notes [3,4] with the most common claims. Maybe someone will find them useful!