Constructive Approximation by Superposition of Sigmoidal Functions (Analysis in Theory and Applications, 2013)
In this paper, a constructive theory is developed for approximating functions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the $L^p$ norm. Results for the simultaneous approximation, with the same order of accuracy, of a function and its derivatives (whenever these exist), are obtained. The relation with neural networks and radial basis functions approximations is discussed. Numerical examples are given for the purpose of illustration.
Keywords: Sigmoidal functions; multivariate approximation; $L^p$ approximation; neural networks; radial basis functions.