Title :
Neural networks for localized approximation of real functions
Author_Institution :
Dept. of Math., California State Univ., Los Angeles, Ca, USA
Abstract :
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
Keywords :
approximation theory; function approximation; neural nets; splines (mathematics); wavelet transforms; Chui-Wang wavelets; bounded derivatives; localized approximation; multivariate analogues; neural networks; real function approximation; spline approximation; Approximation algorithms; Mathematics; Neural networks; Neurons; Polynomials; Spline;
Conference_Titel :
Neural Networks for Processing [1993] III. Proceedings of the 1993 IEEE-SP Workshop
Conference_Location :
Linthicum Heights, MD
Print_ISBN :
0-7803-0928-6
DOI :
10.1109/NNSP.1993.471870
