The multidimensional function approximation based on constructive wavelet RBF neural network

Authors:
Hou Muzhou;Han Xuli
Affiliations:
School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410083, China and School of Information Science and Engineering, Central South University, Changsha 410 ...;School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410083, China
Venue:
Applied Soft Computing
Year:
2011

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Abstract

For the multidimensional continuous function, using constructive feedforward wavelet RBF neural network, we prove that a wavelet RBF neural network with n+1 hidden neurons can interpolate n+1 multidimensional samples with zero error. Then we prove they can uniformly approximate any continuous multidimensional function with arbitrary precision. This method can avoid the defects of conventional neural networks using learning algorithm in practice. The correctness and effectiveness are verified through four numeric experiments.