Synthesis of feedforward networks in supremum error bound.

The main result of this paper is a constructive proof of a formula for the upper bound of the approximation error in Linfinity (supremum norm) of multidimensional 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.