605 RWTH Publication No: 956705        2021       
TITLE Polynomial Approximation of Symmetric Functions
AUTHORS Markus Bachmayr, Geneviève Dusson, Christoph Ortner, Jack Thomas
ABSTRACT We study the polynomial approximation of symmetric multivariate functions and of multi-set functions. Specifically, we consider f(x1,…,xN), where xi∈Rd, 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.
DOI 10.1090/mcom/3868