基于B样条神经网络算子的散乱数据插值  

Interpolation for scattered data with B-spline neural network operators

作　　者：徐慧芳 曹飞龙 XU Huifang;CAO Feilong(College of Sciences,China Jiliang University,Hangzhou 310018,China)

机构地区：[1]中国计量大学理学院

出　　处：《中国计量大学学报》2019年第4期506-513,523,共9页Journal of China University of Metrology

基　　金：国家自然科学基金项目(No.61672477)

摘　　要：目的:研究散乱数据神经网络算子的插值逼近性。方法:首先,将一维B样条函数变换成一类Sigmoid函数。然后,将若干个上述Sigmoid函数相乘得到的多元函数作为激活函数。结果:构造了一类多元神经网络插值算子,以函数的光滑模作为逼近度量,借助散乱数据网格范数,估计该类神经网络算子对有界域上的多元连续函数的逼近误差。特别地,给出一些具体的数值仿真算例进一步验证理论结果。结论:B样条神经网络算子对散乱数据有较好的插值逼近性。Aims: This paper aims to study the interpolation of scattered data by neural network operators. Methods: These neural network operators were activated by the well-known B-spline functions. Results: A class of interpolation operators for multivariate neural networks was constructed. Using the modulus of smoothness of the function and the mesh norm scattered data as a measure of approximation, we proved the uniform approximation theorem and estimated the approximation errors for multivariate continuous function defined on compact sets. In particular, we demonstrated some numerical results to confirm our theorem. Conclusions: B-spline neural network operators have better interpolation approximation to scattered data.

关 键 词：计量 神经网络 插值 散乱数据 B样条函数 逼近误差 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]