Incremental approximation by one-hidden-layer neural networks: discrete functions rapprochement

We characterize incremental approximation of discrete functions by using a one-hidden-layer neural network. The functions to be approximated are represented by a set of input/output pairs. The network consists of input, hidden and linear output layers. In a series of steps we add units to the hidden layer. In each iteration, parameters of one new hidden unit are determined and also all output weights are recalculated. We examine conditions on convergence and its rate and propose a simple algorithm of one unit parameters tuning. This algorithm uses almost exclusively analytical formulas without involving any searching method