$L^2$ and $L^{\mathrm{\infty }}$ rational approximation

Using recently developed algorithms, we compute and compare best $L^2$ and $L^{\mathrm{\infty }}$ rational approximations of analytic functions on the unit disk. Although there is some theory for these problems going back decades, this may be the first computational study. To compute the $L^2$ best approximations, we employ a new formulation of TF-IRKA in barycentric form.