On the Approximability and Curse of Dimensionality of Certain Classes of High-Dimensional Functions

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-03-22 DOI:10.1137/22m1525193

Christian Rieger, Holger Wendland

引用次数: 0

Abstract

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.

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论若干类高维函数的近似性和维度诅咒

SIAM 数值分析期刊》第 62 卷第 2 期第 842-871 页，2024 年 4 月。摘要本文研究了高维函数的近似性，例如在多体展开和高维模型表示中出现的高维函数。这些函数虽然是高维函数，但可以表示为低维函数的有限和。我们将推导出这类函数的采样不等式，给出关于良好采样点位置的明确建议，并证明这类函数不会受到维度诅咒的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.