An analysis of momentum can be tightened using a combination Chebyshev polynomials of the first and second kind. Through this connection we'll derive one of the most iconic methods in optimization: Polyak momentum.

There's a fascinating link between minimization of quadratic functions and polynomials. A link that goes deep and allows to phrase optimization problems in the language of polynomials and vice versa. Using this connection, we can tap into centuries of research in the theory of polynomials and shed new light on …