@inproceedings{52e47fabb9984502892206f2ed27de43,
title = "On p-Adic differential equations with separation of variables",
abstract = "Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate p-Adic setting to be well-posed. This raises precision concerns: how much precision do we need on the input to compute the output accurately? In the case of ordinary differential equations with separation of variables, we make use of the recent technique of differential precision to obtain optimal bounds on the stability of the Newton iteration. The results apply, for example, to algorithms for manipulating algebraic numbers over finite fields, for computing isogenies between elliptic curves or for deterministically finding roots of polynomials in finite fields. The new bounds lead to significant speedups in practice.",
keywords = "Newton iteration, Ordinary differential equation, differential precision, numerical stability, p-Adic numbers",
author = "Pierre Lairez and Tristan Vaccon",
note = "Publisher Copyright: {\textcopyright} 2016 Copyright held by the owner/author(s).; 41st ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2016 ; Conference date: 20-07-2016 Through 22-07-2016",
year = "2016",
month = jul,
day = "20",
doi = "10.1145/2930889.2930912",
language = "English",
series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",
publisher = "Association for Computing Machinery",
pages = "319--323",
editor = "Markus Rosenkranz",
booktitle = "ISSAC 2016 - Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation",
}