Algebraic properties of robust Padé approximants

In the present paper we provide a proof for forward stability (or robustness) and show the absence of spurious poles for the subclass of so-called well-conditioned Padé approximants. We also give a numerical example of some robust Padé approximant which has spurious poles and discuss related questions. It turns out that it is not sufficient to discuss only linear algebra properties of the underlying rectangular Toeplitz matrix, since in our results other matrices like Sylvester matrices also occur. These types of matrices have been used before in numerical greatest common divisor computations.