The main result of this paper is a constructive proof of a formula for the upper bound of the approximation error in L_\infty (supremum norm) of multi-dimensional functions by feedforward networks with one hidden layer of sigmoidal units and a linear output. This result is applied to formulate a new method of neural network synthesis. The result can also be used to estimate complexity of the maximum-error network and/or to initialize that network weights. An example of the network synthesis is given.

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Last modified January 20, 2014.