On the Error of Random Sampling: Uniformly Distributed Random Points on Parametric Curves - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2022

On the Error of Random Sampling: Uniformly Distributed Random Points on Parametric Curves

Abstract

Given a parametric polynomial curve γ:[a,b] →Rn, how can we sample a random point x ∈ im(γ) in such a way that it is distributed uniformly with respect to the arc-length? Unfortunately, we cannot sample exactly such a point---even assuming we can perform exact arithmetic operations. So we end up with the following question: how does the method we choose affect the quality of the approximate sample we obtain? In practice, there are many answers. However, in theory, there are still gaps in our understanding. In this paper, we address this question from the point of view of complexity theory, providing bounds in terms of the size of the desired error.
Fichier principal
Vignette du fichier
2203.02832(2).pdf (801.75 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03601563 , version 1 (25-07-2022)

Identifiers

Cite

Apostolos Chalkis, Christina Katsamaki, Josué Tonelli-Cueto. On the Error of Random Sampling: Uniformly Distributed Random Points on Parametric Curves. ISSAC '22 - International Symposium on Symbolic and Algebraic Computation, Jul 2022, Villeneuve-d'Ascq, France. ⟨10.1145/3476446.3536190⟩. ⟨hal-03601563⟩
34 View
22 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More