Computing the $N$-th Term of a $q$-Holonomic Sequence - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2020

Computing the $N$-th Term of a $q$-Holonomic Sequence

Alin Bostan
  • Fonction : Auteur
  • PersonId : 831654

Résumé

In 1977, Strassen invented a famous baby-step / giant-step algorithm that computes the factorial $N!$ in arithmetic complexity quasi-linear in $\sqrt{N}$. In 1988, the Chudnovsky brothers generalized Strassen’s algorithm to the computation of the $N$-th term of any holonomic sequence in the same arithmetic complexity. We design $q$-analogues of these algorithms. We first extend Strassen’s algorithm to the computation of the $q$-factorial of $N$, then Chudnovskys' algorithm to the computation of the $N$-th term of any $q$-holonomic sequence. Both algorithms work in arithmetic complexity quasi-linear in~$\sqrt{N}$. We describe various algorithmic consequences, including the acceleration of polynomial and rational solving of linear $q$-differential equations, and the fast evaluation of large classes of polynomials, including a family recently considered by Nogneng and Schost.
Fichier principal
Vignette du fichier
Bostan20-arxiv.pdf (758.91 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02882885 , version 1 (27-06-2020)

Identifiants

Citer

Alin Bostan. Computing the $N$-th Term of a $q$-Holonomic Sequence. ISSAC 2020 - 45th International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Greece. pp.8, ⟨10.1145/3373207.3404060⟩. ⟨hal-02882885⟩
93 Consultations
518 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More