Accession Number : ADA312790

Title :   Surface Fitting with Radial Basis Functions and Applications to Neural Networks.

Descriptive Note : Final rept. 1 Jun 92-14 Aug 95,

Corporate Author : TEXAS ENGINEERING EXPERIMENT STATION COLLEGE STATION

Personal Author(s) : Narcowich, Francis J. ; Ward, Joseph D.

PDF Url : ADA312790

Report Date : 12 OCT 1995

Pagination or Media Count : 8

Abstract : Summary. The following is a summary of the research of F. J. Narcowich and J. D. Ward supported by the Air Force during the period 6-92 through 8-95. Results dealing with center placement and stability for neural networks that employ radial basis functions (RBFs) were obtained, and led to convergent RBF identification algorithms with persistently excited regressor vector. A class of RBF-based methods that are grid-free and dimension-blind and that allow one to solve virtually any surface-fitting problem involving derivative information at scattered sites was discovered. For situations where the underlying geometries are noneuclidean-spheres or tori, for example, basis functions analogous to RBFs were developed; these provide tools to fit not only scattered data, but also scattered derivative-data. A class of nonstationary, orthogonal, well-localized periodic scaling functions and wavelets were constructed out of these bases, so that an integrated approach to handling both the representation and analysis of periodic data, even when the data are scattered or noisy, is provided.

Descriptors :   *ALGORITHMS, *NEURAL NETS, *COMPUTER ARCHITECTURE, *PATTERN RECOGNITION, COMPUTER PROGRAMS, SCATTERING, AIR FORCE, IDENTIFICATION, EMPLACEMENT, VECTOR ANALYSIS, HANDLING, FITTINGS.

Subject Categories : Numerical Mathematics
      Computer Hardware

Distribution Statement : APPROVED FOR PUBLIC RELEASE