Approximation by approximate interpolation neural networks with single hidden layer

A bounded function φ defined on (-∞, + ∞) is called general sigmoidal function if it satisfies lim_x→+∞φ(x) = M, lim_x→-∞φ(x) = m. Using the general sigmoidal function as the activation function, a type of neural networks with single hidden layer and n + 1 hidden neurons is constructed. These networks are called approximate interpolation networks, which can approximately interpolate, with arbitrary precision, any set of distinct data in one dimension. By using the modulus of continuity of function as metric, the errors of approximation by the constructed networks is estimated.