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Minimal solutions of the rational interpolation problem

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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 μ-basis of a polynomial planar parametrization in terms of a critical degree arising in the EEA.

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Revista de la Union Matematica Argentina, 2020, vol. 61, num. 2, p. 413-429

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cc-by (c) Cortadellas Benítez, Teresa et al., 2020

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Minimal solutions of the rational interpolation problem