Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions
| Autor: | Frédéric Chyzak, Bruno Salvy, Pierre Lairez, Alin Bostan |
|---|---|
| Přispěvatelé: | Symbolic Special Functions : Fast and Certified (SPECFUN), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Arithmetic and Computing (ARIC), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), ANR-14-CE25-0018,Fast Relax,Approximation rapide et fiable(2014), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Symbolic Computation [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC] Hermite polynomials Generalization 010102 general mathematics ACM: I.: Computing Methodologies/I.1: SYMBOLIC AND ALGEBRAIC MANIPULATION/I.1.2: Algorithms 010103 numerical & computational mathematics Rational function Function (mathematics) Symbolic Computation (cs.SC) Differential operator 01 natural sciences I.1.2 Reduction (complexity) Simple (abstract algebra) ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Applied mathematics 0101 mathematics Symbolic integration Mathematics |
| Zdroj: | ISSAC 2018-International Symposium on Symbolic and Algebraic Computation ISSAC 2018-International Symposium on Symbolic and Algebraic Computation, Jul 2018, New York, United States. pp.1-8, ⟨10.1145/3208976.3208992⟩ |
| DOI: | 10.1145/3208976.3208992⟩ |
| Popis: | Hermite reduction is a classical algorithmic tool in symbolic integration. It is used to decompose a given rational function as a sum of a function with simple poles and the derivative of another rational function. We extend Hermite reduction to arbitrary linear differential operators instead of the pure derivative, and develop efficient algorithms for this reduction. We then apply the generalized Hermite reduction to the computation of linear operators satisfied by single definite integrals of D-finite functions of several continuous or discrete parameters. The resulting algorithm is a generalization of reduction-based methods for creative telescoping. Accepted for publication in the proceedings of the conference ISSAC'18 (Jul 16-19, 2018) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|