Rational functions and the AAA algorithm

Much of mathematics starts from polynomials, but rational functions have a special power because their poles are not constrained all to lie at infinity. Until recently, there was no reliable method to construct rational approximations to functions on real and complex sets. This has changed with the appearance of the AAA algorithm (Nakatsukasa-SeteT. 2018). We will present the algorithm and demonstrate a number of applications, including data fitting, analytic continuation, and the solution of PDEs