The minimal solutions of the rational interpolation problem

Autores: Teresa Cortadellas Benítez, Carlos D'Andrea , Mª Eulalia Montoro López
Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 43, 2018 (Ejemplar dedicado a: Proceedings of the XVI EACA Zaragoza Encuentros de Algebra Computacional y Aplicaciones), págs. 79-82
Idioma: inglés
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Resumen
- We look for minimal solutions of the rational interpolation problem y (j) (xi) = yi,j in terms of two different degrees. The space of rational functions y = a b interpolating a given set of points can be parameterized keeping track the degrees δ(y) = max{deg a, deg b} and κ(y) = deg a + deg b. In both cases the minimal solutions, the rational interpolating functions with smallest degree, can be expressed in terms of the Euclidean algorithm. We review these results and prove those related with the δ degree in the framework of syzygies