Mean Dimension of Radial Basis Functions

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-05-21 DOI:10.1137/23m1614833

Christopher Hoyt, Art B. Owen

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1191-1211, June 2024.
Abstract. We show that generalized multiquadric radial basis functions (RBFs) on [math] have a mean dimension that is [math] as [math] with an explicit bound for the implied constant, under moment conditions on their inputs. Under weaker moment conditions the mean dimension still approaches 1. As a consequence, these RBFs become essentially additive as their dimension increases. Gaussian RBFs by contrast can attain any mean dimension between 1 and [math]. We also find that a test integrand due to Keister that has been influential in quasi-Monte Carlo theory has a mean dimension that oscillates between approximately 1 and approximately 2 as the nominal dimension [math] increases.

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径向基函数的平均维度

SIAM 数值分析期刊》第 62 卷第 3 期第 1191-1211 页，2024 年 6 月。摘要。我们证明，在输入矩条件下，[math] 上的广义多四边形径向基函数 (RBF) 的平均维度与[math] 的平均维度相同，且隐含常数有明确的约束。在较弱的力矩条件下，平均维数仍然接近 1。因此，随着维度的增加，这些 RBF 本质上变成了加法。相比之下，高斯 RBF 的平均维数可以达到 1 和 [math] 之间的任意维数。我们还发现，基斯特（Keister）提出的一个测试积分在准蒙特卡罗理论中很有影响力，随着标称维度[math]的增加，其平均维度在大约 1 和大约 2 之间摇摆。

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.