Work

Complexity Estimates for Two Uncoupling Algorithms

Year: 2013

Type: article

Abstract: Uncoupling algorithms transform a linear differential system of first order into one or several scalar differential equations. We examine two approaches to uncoupling: the cyclic-vector method (CVM) and the Danilevski-Barkatou-Zürcher algorithm (DBZ). We give tight size bounds on the scalar equations produced by CVM, and design a fast variant of CVM whose complexity is quasi-optimal with respect to the output size. We exhibit a strong structural link between CVM and DBZ enabling to show that, in the generic case, DBZ has polynomial complexity and that it produces a single equation, strongly related to the output of CVM. We prove that algorithm CVM is faster than DBZ by almost two orders of magnitude, and provide experimental results that validate the theoretical complexity analyses.

DOI: 10.48550/arxiv.1301.5414

Authors: Bostan, Alin, Chyzak, Frédéric, De Panafieu, Élie

Institutions: Institut national de recherche en sciences et technologies du numérique, Centre Inria de Saclay, Laboratoire d'Informatique Algorithmique: Fondements et Applications

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Institut national de recherche en informatique et en automatique (INRIA)

OpenAlex ID: W2952868084

FWCI: 1.058

Cites: 22

Cited by: 6

Related to: 20