@inproceedings{BoChLiSa12,
author = {Bostan, Alin and Chyzak, Fr{\'e}d{\'e}ric and Li, Ziming and Salvy, Bruno},
title = {Fast Computation of Common Left Multiples of Linear
Ordinary Differential Operators},
booktitle = {ISSAC '12: Proceedings of the twenty-fifth International
Symposium on Symbolic and Algebraic Computation},
year = {2012},
editor = {van Hoeij, Mark and van der Hoeven, Joris},
pages = {99--106},
arxiv = {abs/1205.0879},
abstract = {We study tight bounds and fast algorithms for LCLMs of
several linear differential operators with polynomial coefficients. We
analyze the arithmetic complexity of existing algorithms for LCLMs, as well
as the size of their outputs. We propose a new algorithm that recasts the
LCLM computation in a linear algebra problem on a polynomial matrix. This
algorithm yields sharp bounds on the coefficient degrees of the LCLM,
improving by one order of magnitude the best bounds obtained using previous
algorithms. The complexity of the new algorithm is almost optimal, in the
sense that it nearly matches the arithmetic size of the output.},
}