Polynomial Approximation of Symmetric Functions

09/30/2021

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by   Markus Bachmayr, et al.

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We study the polynomial approximation of symmetric multivariate functions. Specifically, we consider f(x_1, …, x_N), where x_i ∈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.