Lp空间中神经网络逼近的几何速度

数学物理学报 ›› 2010, Vol. 30 ›› Issue (3): 848-856.

L^p空间中神经网络逼近的几何速度

俞国华

宁波大学理学院浙江宁波315211

收稿日期:2007-12-11 修回日期:2009-12-22 出版日期:2010-05-25 发布日期:2010-05-25
基金资助:
国家自然科学基金(10471069)和浙江省教育厅科研基金(20051778)资助

The Geometric Rate of Approximation of Neural Network in L^p-Space

YU Guo-Hua

Faculty of Science, Ningbo University, Zhejiang Ningbo 315211

Received:2007-12-11 Revised:2009-12-22 Online:2010-05-25 Published:2010-05-25
Supported by:
国家自然科学基金(10471069)和浙江省教育厅科研基金(20051778)资助

摘要/Abstract

摘要：

该文主要研究了L^p空间中神经网络逼近的几何速度. 将凸贪婪迭代法应用于L^p空间中满足"δ -角度的条件"的一类函数. 作者将文献[1] 的结论推广到L^p空间中, 得到当0 < q <1时人工神经网络逼近的速度是o(qⁿ).

关键词: 神经网络, L^p-空间, 逼近, 几何速度

Abstract:

This paper is devoted to the investigation of approximation of neural network in L^p-space. The convex greedy iteration method is applied to a class of functions that satisfy the so-called "δ-angular condition'' in L^p-space. We show that the rate of approximation is of order o(qⁿ) for some 0<q<1, which extends the result of [1] to L^p-space.

Key words: Neural networks, L^p-space, Approximation, Geometric rate

中图分类号:

41A20

俞国华. L^p空间中神经网络逼近的几何速度[J]. 数学物理学报, 2010, 30(3): 848-856.

YU Guo-Hua. The Geometric Rate of Approximation of Neural Network in L^p-Space[J]. Acta mathematica scientia,Series A, 2010, 30(3): 848-856.

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