Revista de la
Unión Matemática Argentina
Minimal solutions of the rational interpolation problem
Teresa Cortadellas Benítez, Carlos D'Andrea, and Eulàlia Montoro
Volume 61, no. 2 (2020), pp. 413–429

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We explore connections between the approach of solving the rational interpolation problem via resolutions of ideals and syzygies, and the standard method provided by the Extended Euclidean Algorithm (EEA). As a consequence, we obtain explicit descriptions for solutions of minimal degrees in terms of the degrees of elements appearing in the EEA. This result allows us to describe the minimal degree in a $\mu$-basis of a polynomial planar parametrization in terms of a critical degree arising in the EEA.