Polynomial approximation of symmetric functions

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2023-06-28 DOI:10.1090/mcom/3868

Markus Bachmayr, Geneviève Dusson, Christoph Ortner

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引用次数: 0

Abstract

We study the polynomial approximation of symmetric multivariate functions and of multi-set functions. Specifically, we consider f ( x 1 , … , x N ) f(x_1, \dots , x_N) , where x i ∈ R d x_i \in \mathbb {R}^d , and f f is invariant under permutations of its N 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 f , and in particular study the dependence of that ratio on d , N 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 N becomes a parameter of the input.

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对称函数的多项式近似

研究了对称多元函数和多集函数的多项式逼近问题。具体地说，我们考虑f(x 1，…，x N) f(x_1， \dots, x_N)，其中x i∈R d x_i \in \mathbb {R}^d, f f在其N N个参数的置换下是不变的。我们演示了如何利用这些对称性来提高函数f的多项式近似中的成本与错误率，并特别研究了该比率对d, N, N和多项式度的依赖。然后，这些结果用于构造近似并证明在多集上定义的函数的近似率，其中N N成为输入的参数。

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464