Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
A Method to Solve Fredholm Integral Equations of the First Kind by Using a Neural Network
Qing PUShinzo KITAMURA
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1989 Volume 2 Issue 10 Pages 350-356

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Abstract

Inverse problems are often encountered in various fields of engineering. A method is proposed in this paper to obtain a solution for the Fredholm integral equations of the first kind, which define a typical case of inverse problems. The method uses a neural network which is able to learn the inverse mapping from the output. function to input function of the integral equation under some a priori information on relevant problems. The network which has terminated its learning successfully can be expected to give a reasonable solution for not-learned input data from its association functions. It was shown for the cases of Phillips' example and of the size distribution measurement of aerosol particles by multi-wavelength laser radar that the method yields rather more stable solutions as compared with those by the conventional regularization method.

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