On the complexity of solving polynomial initial value problems - Archive ouverte HAL Access content directly
Conference Papers Year : 2012

On the complexity of solving polynomial initial value problems

(1) , (2) , (1)
1
2

Abstract

In this paper we prove that computing the solution of an initial-value problem $\dot{y}=p(y)$ with initial condition $y(t_0)=y_0\in\R^d$ at time $t_0+T$ with precision $e^{-\mu}$ where $p$ is a vector of polynomials can be done in time polynomial in the value of $T$, $\mu$ and $Y=\sup_{t_0\leqslant u\leqslant T}\infnorm{y(u)}$. Contrary to existing results, our algorithm works for any vector of polynomials $p$ over any bounded or unbounded domain and has a guaranteed complexity and precision. In particular we do not assume $p$ to be fixed, nor the solution to lie in a compact domain, nor we assume that $p$ has a Lipschitz constant.
Fichier principal
Vignette du fichier
complexity_solving_pivp.pdf (294.95 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00760742 , version 1 (04-12-2012)

Identifiers

  • HAL Id : hal-00760742 , version 1

Cite

Olivier Bournez, Daniel Graça, Amaury Pouly. On the complexity of solving polynomial initial value problems. International Symposium on Symbolic and Algebraic Computation (ISSAC'12), 2012, France. ⟨hal-00760742⟩
101 View
85 Download

Share

Gmail Facebook Twitter LinkedIn More