Conversions between barycentric, RKFUN, and Newton representations of rational interpolants

We derive explicit formulas for converting between rational interpolants in barycentric, rational Krylov (RKFUN), and Newton form. We show applications of these conversions when working with rational approximants produced by the AAA algorithm [Y. Nakatsukasa, O. S`ete, L. N. Trefethen, arXiv preprint 1612.00337, 2016] within the Rational Krylov Toolbox and for the solution of nonlinear eigenvalue problems.