SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 842-871, April 2024.
Abstract. In this paper, we study the approximability of high-dimensional functions that appear, for example, in the context of many body expansions and high-dimensional model representation. Such functions, though high-dimensional, can be represented as finite sums of lower-dimensional functions. We will derive sampling inequalities for such functions, give explicit advice on the location of good sampling points, and show that such functions do not suffer from the curse of dimensionality.

中文翻译：

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论某类高维函数的逼近性与维数灾难

《SIAM 数值分析杂志》，第 62 卷，第 2 期，第 842-871 页，2024 年 4 月。
摘要。在本文中，我们研究了在许多身体扩展和高维模型表示的背景下出现的高维函数的近似性。此类函数虽然是高维的，但可以表示为低维函数的有限和。我们将导出此类函数的采样不等式，对良好采样点的位置给出明确的建议，并证明此类函数不会受到维数灾难的影响。