用伯恩斯坦算子逼近重现核希尔伯特空间函数

IF 1.1 3区数学 Q1 MATHEMATICS

Results in Mathematics Pub Date : 2024-08-30 DOI:10.1007/s00025-024-02253-w

Han Feng, Sonia Y. W. Hui, Ruohan Shen

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引用次数: 0

摘要

受机器学习理论中核方法的启发，我们研究了伯恩斯坦算子对再现核希尔伯特空间中函数的均匀逼近。我们根据再现核希尔伯特空间中的函数规范提供了逼近率。此外，还介绍了伯恩斯坦算子收缩特性的案例研究。

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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Approximating Reproducing Kernel Hilbert Space Functions by Bernstein Operators

Motivated by kernel methods in machine learning theory, we study the uniform approximation of functions from reproducing kernel Hilbert spaces by Bernstein operators. Rates of approximation are provided in terms of the function norm in the reproducing kernel Hilbert space. A case study of contracting properties of the Bernstein operators is also presented.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.