Mustansiriyah Journal of Pure and Applied Sciences

L_P Approximation by Fixed Weighted Neural Network

S. S. Mahdi

E. S. Bhaya

DOI: https://doi.org/10.47831/mjpas.v1i2.31

Keywords: L_p norm, Neural network, Approximated, Approximated function, Best approximation.

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Abstract

 Neural networks are tools for parallel computations of functions with several variables, it is a linear computation of non-linear functions that we are call activation functions. In our paper we deal with one hidden layer feed forward neural network.

We have two problems with neural networks approximation, the first is the density problem concerns. With the condition for the approximated function to approximate by the neural networks. In previous works on approximation using neural networks, the weights are different for each input. This makes engineering applications very difficult.

In this work we approximate any bounded function on   for  by a forward neural network and find the degree of the best approximation by this neural network using the k’ th order of smoothness. Then we connect neurons number and the degree of the best approximation.