Matrix rational interpolation with poles as interpolation points
M.\ Van Barel, B.\ Beckermann, A.\ Bultheel & G.\ Labahn
Nonlinear Numerical Methods and Rational Approximation, (A. Cuyts ed.), Kluwer Academic Publishers, (1994) 137-148.

In this paper, we show the equivalence between matrix rational interpolation problems with poles as interpolation points and no-pole problems. This equivalence provides an effective method for computing matrix rational interpolants having poles as interpolation points. However, this equivalence is only valid in those cases where enough pole information is known. It is an open problem on how one can transform the pole problem to a no-pole problem in other cases.