In this paper, the technique of approximate partition of unity is used to construct a class of neural networks operators with sigmoidal functions. Using the modulus of continuity of function as a metric, the errors of...In this paper, the technique of approximate partition of unity is used to construct a class of neural networks operators with sigmoidal functions. Using the modulus of continuity of function as a metric, the errors of the operators approximating continuous functions defined on a compact interval are estimated. Furthmore, Bochner-Riesz means operators of double Fourier series are used to construct networks operators for approximating bivariate functions, and the errors of approximation by the operators are estimated.展开更多
Recently,Li[16]introduced three kinds of single-hidden layer feed-forward neural networks with optimized piecewise linear activation functions and fixed weights,and obtained the upper and lower bound estimations on th...Recently,Li[16]introduced three kinds of single-hidden layer feed-forward neural networks with optimized piecewise linear activation functions and fixed weights,and obtained the upper and lower bound estimations on the approximation accuracy of the FNNs,for continuous function defined on bounded intervals.In the present paper,we point out that there are some errors both in the definitions of the FNNs and in the proof of the upper estimations in[16].By using new methods,we also give right approximation rate estimations of the approximation by Li’s neural networks.展开更多
基金Supported by the National Natural Science Foundation of China(61179041, 61101240)the Zhejiang Provincial Natural Science Foundation of China(Y6110117)
文摘In this paper, the technique of approximate partition of unity is used to construct a class of neural networks operators with sigmoidal functions. Using the modulus of continuity of function as a metric, the errors of the operators approximating continuous functions defined on a compact interval are estimated. Furthmore, Bochner-Riesz means operators of double Fourier series are used to construct networks operators for approximating bivariate functions, and the errors of approximation by the operators are estimated.
文摘Recently,Li[16]introduced three kinds of single-hidden layer feed-forward neural networks with optimized piecewise linear activation functions and fixed weights,and obtained the upper and lower bound estimations on the approximation accuracy of the FNNs,for continuous function defined on bounded intervals.In the present paper,we point out that there are some errors both in the definitions of the FNNs and in the proof of the upper estimations in[16].By using new methods,we also give right approximation rate estimations of the approximation by Li’s neural networks.
