Session III.2 - Approximation Theory
Poster
Polynomial Approximation of Symmetric Functions
Geneviève Dusson
CNRS & Université Franche-Comté, France - This email address is being protected from spambots. You need JavaScript enabled to view it.
In this poster, I will present a recent work [1] on the polynomial approximation of symmetric multivariate functions and of multiset functions. More precisely, I will consider functions that are invariant with respect to the permutations of its N variables, each one being d-dimensional, and I will show how these symmetries can be exploited to improve the cost versus error ratio when the function is approximated by polynomials. I will then mention how these results can be used for deriving approximation rates for functions defined on multisets, that it where N becomes a parameter of the input.
[1] Bachmayr, M., Dusson, G., Ortner, C., Thomas, J.: Polynomial Approximation of Symmetric Functions, http://arxiv.org/abs/2109.14771, (2021)
Joint work with Markus Bachmayr (RWTH Aachen, Germany), Christoph Ortner (UBC, Canada) and Jack Thomas (University of Warwick, UK).