The estimate for approximation error of neural networks: A constructive approach

Neural networks are widely used in many applications including astronomical physics, image processing, recognition, robotics and automated target tracking, etc. Their ability to approximate arbitrary functions is the main reason for this popularity. The main result of this paper is a constructive proof of a formula for the upper bound of the approximation error by feedforward neural networks with one hidden layer of sigmoidal units and a linear output. The result can also be used to estimate complexity of the maximum error network. An example to demonstrate the theoretical result is given.