Approximation by neural networks iterates

Abstract

Here we study the multivariate quantitative approximation of real valued continuous multivariate functions on a box or RN, N ∈ N, by the multivariate quasi-interpolation sigmoidal and hyperbolic tangent iterated neural network operators. This approximation is derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order partial derivatives. Our multivariate iterated operators are defined by using the multidimensional density functions induced by the logarithmic sigmoidal and the hyperbolic tangent functions. The approximations are pointwise and uniform. The related feed-forward neural networks are with one hidden layer. © Springer Science+Business Media New York 2013.