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 L-infinity (supremum norm) of mul tidimensional functions by feedforward networks with one hidden layer of si gmoidal units and a linear output. This result is applied to formulate a ne w method of neural-network synthesis. The result can also be used to estima te complexity of the maximum-error network and/or to initialize that networ k weights. An example of the network synthesis is given.