A new approach to the rational interpolation problem

摘要

We shall reformulate the classical Newton-Padé rational interpolation problem (NPRIP) to take away several drawbacks of the Newton-Padé approach. A new recursive algorithm, not reordering the interpolation points, will be designed, enabling us to give a parametrization of all solutions, not only for the linearized RIP but also for the proper RIP. This paper generalizes our earlier work where the Padé approximation problem, i.e., when all the interpolation points coincide at the origin, was solved by reformulating it as a minimal partial realization problem (Van Barel (1989), Van Barel and Bultheel (1989)).