On simultaneous approximations by radial basis function neural networks

摘要

It is shown in this paper by a constructive method that any multivariate function and all its existing derivatives can be simultaneously approximated by a radial basis function (RBF) neural network, where the assumptions on the RBFs are relatively mild. By considering the translations of RBFs, it is proved that an O(m−12) order of simultaneous approximations to a certain class of functions can be achieved by using a translation network with just m neurons.