Minimal solutions of the rational interpolation problem

Authors

  • Teresa Cortadellas Benítez Universitat de Barcelona, Facultat d’Educació. Passeig de la Vall d’Hebron 171, 08035 Barcelona, Spain
  • Carlos D'Andrea Universitat de Barcelona, Departament de Matemàtiques i Informàtica, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
  • Eulàlia Montoro Universitat de Barcelona, Departament de Matemàtiques i Informàtica, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain

DOI:

https://doi.org/10.33044.revuma/v61n2a14

Abstract

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.

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Published

2020-12-23

Issue

Vol. 61 No. 2 (2020)

Section

Article

License

Copyright (c) 2023 Teresa Cortadellas Benítez, Carlos D'Andrea, Eulàlia Montoro

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