Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy.
Neural Netw. 2015 Jul;67:28-36. doi: 10.1016/j.neunet.2015.02.002. Epub 2015 Feb 8.
In this paper, the interpolation of multivariate data by operators of the neural network type is proved. These operators can also be used to approximate continuous functions defined on a box-domain of R(d). In order to show this fact, a uniform approximation theorem with order is proved. The rate of approximation is expressed in terms of the modulus of continuity of the functions being approximated. The above interpolation neural network operators are activated by suitable linear combinations of sigmoidal functions constructed by a procedure involving the well-known central B-spline. The implications of the present theory with the classical theories of neural networks and sampling operators are analyzed. Finally, several examples with graphical representations are provided.
本文证明了通过神经网络类型的算子对多元数据进行插值。这些算子也可以用于逼近 R(d) 中盒域上定义的连续函数。为了证明这一事实，证明了一个具有阶的一致逼近定理。逼近的速率用被逼近函数的连续模来表示。上述插值神经网络算子是通过涉及著名的中心 B 样条的过程构建的可激活的 sigmoidal 函数的适当线性组合来激活的。分析了该理论与神经网络和采样算子的经典理论的关系。最后，提供了几个带有图形表示的示例。
