Surface Fitting via Radial and Related Basis Functions with Applications to Neural Networks

Abstract

Progress was made along several fronts during this period. Classes of RBF, periodic, and nonstationary spherical wavelets were constructed, all being capable of synthesizing and analyzing scattered data. Shape preservation problems were investigated. A framework for obtaining rates of approximation in non-traditional settings and data - i.e. compact manifolds and generalized Hermite data, was provided. This framework was used to derive approximation rates for various classes of functions on the circle and the 2-sphere. In particular, for a broad class of functions, rates of approximation were obtained for scattered data on the m-sphere. Stability questions related to these classes of functions were studied. Results from the work above were applied to neural networks.

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Document Details

Document Type
Technical Report
Publication Date
Feb 25, 1998
Accession Number
ADA342010

Entities

People

  • Francis J. Narcowich
  • Joseph D. Ward

Organizations

  • Texas A&M University

Tags

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Algorithms
  • Computer Programs
  • Computing-Related Activities
  • Convex Sets
  • Coordinate Systems
  • Data Science
  • Data Sets
  • Harmonic Analysis
  • Hilbert Space
  • Interpolation
  • Mathematics
  • Neural Networks
  • Periodic Functions
  • Universities
  • Word Processors

Readers

  • Graph Algorithms and Convex Optimization.
  • Neural Network Machine Learning.
  • Systems Analysis and Design

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms
  • AI & ML - Neural Networks