Neural networks for localized approximation /

Bibliographic Details
Main Authors:	Chui, C. K. (Author), Li, Xin (Author), Mhaskar, H. N. (Hrushikesh Narhar), 1956- (Author)
Corporate Authors:	National Science Foundation (U.S.) (sponsoring body.), United States. Army Research Office (sponsoring body.), United States. Air Force. Office of Scientific Research (sponsoring body.)
Format:	Book
Language:	English
Published:	College Station, Texas : Center for Approximation Theory, Department of Mathematics, Texas A & M University, 1993.
Series:	CAT report ; no. 289.
Subjects:	Neural networks (Computer science) Wavelets (Mathematics) Spline theory. Approximation theory. Approximations and expansions > Approximations and expansions > Multidimensional problems. Approximations and expansions > Approximations and expansions > Approximation by other special function classes. Information and communication, circuits > Circuits, networks > None of the above, but in this section. Sigmoidal functions

Description
Abstract:	We prove that feedforward artificial neural networks with a single hidden layer and an ideal sigmoidal response function cannot provide localized approximation in a Euclidean space of dimension higher than one. We also show that networks with two hidden layers can be designed to provide localized approximation. Since wavelet bases are most effective for local approximation, we give a discussion of the implementation of spline-wavelets using multilayered networks where the response function is a sigmoidal function of order at least two.
Item Description:	"February, 1993." Funding information taken from page 1.
Physical Description:	21 pages ; 28 cm
Bibliography:	Includes bibliographical references (pages 20-21).