Hermite-Padé approximation (basic notions and theorems)

摘要

Our purpose is to give a brief exposition of basic notions and facts on Hermite-Padé approximation theory. A Hermite-Padé form (HPF) is defined here in the same way as a Padé approximant is. As a consequence, in some cases HPF does not exist. Even in the modified version HPF need not be unique. Therefore it was worthwhile to choose some HPF as the optimal one.All criteria of existence, unicity, etc. are phrased in a unified manner. They base on few quantities depending on the power series under consideration and are usable in the theory rather than in the numerical practice.