Simultaneous Rational Function Reconstruction with Errors: Handling Multiplicities and Poles - HAL UNIV-PARIS8 - open access Accéder directement au contenu
Article Dans Une Revue Journal of Symbolic Computation Année : 2023

Simultaneous Rational Function Reconstruction with Errors: Handling Multiplicities and Poles

Eleonora Guerrini
Kamel Lairedj
  • Fonction : Auteur
  • PersonId : 1131008
Romain Lebreton

Résumé

In this paper, we focus on extensions of methods for interpolating rational functions from their evaluations, in the context of erroneous evaluations. This problem can be seen both from a computer algebra and a coding theory point of view. In computer algebra, this is a generalization of Simultaneous Rational Function Reconstruction with errors and multiprecision evaluations. From an error correcting codes point of view, this problem is related to the decoding of some algebraic codes such as Reed-Solomon, Derivatives or Multiplicity codes. We give conditions on the inputs of the problem which guarantee the uniqueness of the interpolant. Since we deal with rational functions, some evaluation points may be poles: a first contribution of this work is to correct any error in a scenario with poles and multiplicities that extends (Kaltofen et al., 2020). Our second contribution is to adapt rational function reconstruction for random errors, and provide better conditions for uniqueness using interleaving techniques as in (Guerrini et al., 2021).
Fichier principal
Vignette du fichier
GuerriniLairedjLebretonZappatore.pdf (432.56 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03620179 , version 1 (25-03-2022)

Identifiants

Citer

Eleonora Guerrini, Kamel Lairedj, Romain Lebreton, Ilaria Zappatore. Simultaneous Rational Function Reconstruction with Errors: Handling Multiplicities and Poles. Journal of Symbolic Computation, 2023, 116, pp.345-364. ⟨10.1016/j.jsc.2022.10.007⟩. ⟨hal-03620179⟩
156 Consultations
107 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More