Constructive approximation to real function by wavelet neural networks

• Published in: Neural computing & applications Vol. 18; no. 8; pp. 883 - 889
• Main Authors: Muzhou, Hou, Xuli, Han, Yixuan, Gan
• Format: Journal Article
• Language: English
• Published: London Springer-Verlag 01.11.2009; Springer
• Subjects: Applied sciences; Artificial Intelligence; Computational Biology/Bioinformatics; Computational Science and Engineering; Computer Science; Computer science; control theory; systems; Data Mining and Knowledge Discovery; Exact sciences and technology; Fourier analysis; Image Processing and Computer Vision; Learning and adaptive systems; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Original Article; Probability and Statistics in Computer Science; Real functions; Sciences and techniques of general use; Interpolation; Wavelet neural networks; Uniform approximation; Wavelets; Neural computation; Neuron; Error estimation; Wavelet transformation; Real function; Approximation by function; Continuous function; Neural network; Function approximation; Application
• ISSN: 0941-0643; 1433-3058
• DOI: 10.1007/s00521-008-0194-2

We present a type of single-hidden layer feed-forward wavelet neural networks. First, we give a new and quantitative proof of the fact that a single-hidden layer wavelet neural network with n  + 1 hidden neurons can interpolate n  + 1 distinct samples with zero error. Then, without training, we constructed a wavelet neural network X a ( x , A ), which can approximately interpolate, with arbitrary precision, any set of distinct data in one or several dimensions. The given wavelet neural network can uniformly approximate any continuous function of one variable.