Neural networks for localized approximation of real functions

摘要

The problem of constructing universal networks capable of approximating all functions having bounded derivatives is discussed. It is demonstrated that, using standard ideas from the theory of spline approximation, it is possible to construct such networks to provide localized approximation. The networks can be used to implement multivariate analogues of the Chui-Wang wavelets (1990) and also for the simultaneous approximation of a function and its derivative. The number of neurons required to yield the desired approximation at any point does not depend upon the degree of accuracy desired.