.png){kind=icon}
返回
Neural network interpolation operators optimized by Lagrange polynomial?
.png){kind=icon}
PRE
AI
DOI：10.1016/j.neunet.2022.06.007.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
In this paper, we introduce a new type of interpolation operators by using Lagrange polynomials of degree r, which can be regarded as feedforward neural networks with four layers. The approximation rate of the new operators can be estimated by the (r + 1)-th modulus of smoothness of the objective functions. By adding some smooth assumptions on the activation function, we establish two important inequalities of the derivatives of the operators. With these two inequalities, by using the K-functional and Berens-Lorentz lemma in approximation theory, we establish the converse theorem of approximation. We also give the Voronovskaja-type asymptotic estimation of the operators for smooth functions. Furthermore, we extend our operators to the multivariate case, and investigate their approximation properties for multivariate functions. Finally, some numerical examples are given to demonstrate the validity of the theoretical results obtained and the superiority of the operators.(c) 2022 Elsevier Ltd. All rights reserved.
Keyword:
Sigmoidal function
Neural network operators
Interpolation
Uniform approximate
? n
j=1
期刊
IF:
6.3
论文数:
8.2K
被引数:
3.0W
机构
引用论文
On the approximation by single hidden layer feedforward neural networks with fixed weights.png)
NEURAL NETWORKS
OAAI
NEURAL NETWORKSIF6.3
OAAI分享收藏
分享收藏Real-time and offline techniques for identifying obstructive sleep apnea patients用于识别阻塞性睡眠呼吸暂停患者的实时和离线技术
PREAI
分享收藏分享收藏
查看更多内容