单变量Sigmoidal型神经网络的逼近

马国春, 虞旦盛, 周平

数学学报 ›› 2014, Vol. 57 ›› Issue (1) : 89-100.

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数学学报 ›› 2014, Vol. 57 ›› Issue (1) : 89-100. DOI: 10.12386/A2014sxxb0008
论文

单变量Sigmoidal型神经网络的逼近

    马国春1, 虞旦盛1, 周平2
作者信息 +

On Approximation by Univariate Sigmoidal Neural Networks

    Guo Chun MA1, Dan Sheng YU1, Ping ZHOU2
Author information +
文章历史 +

摘要

引入了一种新的sigmoidal型神经网络,给出了其对连续函数逼近的点态和整体估计. 结果表明这种新的神经网络算子具有多项式逼近所不能达到的很好的逼近速度.为了改进对光滑函数的逼近速度,我们进一步引入了一种新的神经网络的线性组合,并给出了这种组合逼近的点态估计和整体估计.最后给出了一个数值例子.

Abstract

We first introduce a new type of neural network operators with sigmoidal functions, and give the pointwise and global estimates of the approximation by the networks. The new neural network operators can approximate the functions with a very good rate which can not be obtained by polynomial approximation. To further improve the approximation rate for functions of smoothness, we also introduce a new type of combinations of neural network operators, and give pointwise and global estimates of the approximation by the combinations. A numerical example is given to demonstrate our new method.

关键词

前向神经网络 / sigmoidal函数 / 逼近速度

Key words

feedforward neural networks / sigmoidal functions / approximation rate

引用本文

导出引用
马国春, 虞旦盛, 周平. 单变量Sigmoidal型神经网络的逼近. 数学学报, 2014, 57(1): 89-100 https://doi.org/10.12386/A2014sxxb0008
Guo Chun MA, Dan Sheng YU, Ping ZHOU. On Approximation by Univariate Sigmoidal Neural Networks. Acta Mathematica Sinica, Chinese Series, 2014, 57(1): 89-100 https://doi.org/10.12386/A2014sxxb0008

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基金

虞旦盛受国家自然科学基金(10901044)和杭州师范大学优秀中青年教师支持计划项目资助;周平受加拿大NSERC资助

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