Polynomial Approximation of Symmetric Functions - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Polynomial Approximation of Symmetric Functions

Markus Bachmayr
  • Fonction : Auteur
Christoph Ortner
  • Fonction : Auteur
Jack Thomas
  • Fonction : Auteur

Résumé

We study the polynomial approximation of symmetric multivariate functions and of multi-set functions. Specifically, we consider $f(x_1, \dots, x_N)$, where $x_i \in \mathbb{R}^d$, and $f$ is invariant under permutations of its $N$ arguments. We demonstrate how these symmetries can be exploited to improve the cost versus error ratio in a polynomial approximation of the function $f$, and in particular study the dependence of that ratio on $d, N$ and the polynomial degree. These results are then used to construct approximations and prove approximation rates for functions defined on multi-sets where $N$ becomes a parameter of the input.

Dates et versions

hal-03846464 , version 1 (10-11-2022)

Identifiants

Citer

Markus Bachmayr, Geneviève Dusson, Christoph Ortner, Jack Thomas. Polynomial Approximation of Symmetric Functions. 2022. ⟨hal-03846464⟩
7 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More