Minimal solutions of the rational interpolation problem

08/07/2018

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by   Teresa Cortadellas Benitez, et al.

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We compute minimal solutions of the rational interpolation problem in terms of different notions of degrees associated to these functions. In all the cases, the rational interpolating functions with smallest degree can be computed via the Extended Euclidean Algorithm and syzygies of polynomials. As a by-product, we describe the minimal degree in a mu-basis of a polynomial planar parametrization in terms of a "critical" degree arising in the EEA.