Approximation with RBF neural networks using unit smoothing factors and translations

The groundbreaking research by Broomhead and Lowe introduced radial basis function neural networks (RBFNNs), which have become widely known because of their remarkable effectiveness in function approximation. Originally created for the purpose of data interpolation in high-dimensional spaces, RBFNNs have since been utilized in a variety of applied areas. In this paper, we consider the approximation of continuous multivariate functions using specially constructed RBFNNs, where the smoothing factors are set to $1$ and additional translations are incorporated. We propose a practically useful formula for the precise computation of the approximation error in the uniform norm.