Fractional neural network approximation
Fractional neural network approximation
复制标题
DOI：
10.1016/j.camwa.2012.01.019
复制
发表时间：
2012-09-01
影响因子：
2.9
通讯作者：
Anastassiou, George A.
中科院分区：
文献类型：
--
作者：
Anastassiou, George A.
本文研究了拟插值S形和双曲正切神经网络算子对紧区间上真实的值函数的一元分数阶定量逼近。这些近似值是通过建立涉及到所涉及的函数的左右Caputo分数阶导数的连续模的杰克逊型不等式得到的。近似是逐点的，并且关于一致范数。相关的前馈神经网络是一个隐藏层。我们的分数阶逼近结果在高阶时比普通的分数阶逼近结果收敛得更好。(c)2012爱思唯尔有限公司保留所有权利。
Here, we study the univariate fractional quantitative approximation of real valued functions on a compact interval by quasi-interpolation sigmoidal and hyperbolic tangent neural network operators. These approximations are derived by establishing Jackson type inequalities involving the moduli of continuity of the right and left Caputo fractional derivatives of the engaged function. The approximations are pointwise and with respect to the uniform norm. The related feed-forward neural networks are with one hidden layer. Our fractional approximation results into higher order converges better than the ordinary ones. (c) 2012 Elsevier Ltd. All rights reserved.