Fast Evaluation of Radial Basis Functions: A Multivariate Momentary Evaluation Scheme

Abstract

This paper presents a scheme for fast evaluation of splines, or 'radial' basis functions, of the form s(.) = p(.) + summation from i = 1 to i = N of function (lambda(i)Phi(. - zi)). Here p is a low degree polynomial and Phi from R(exp n) to R is a function that need not be radial, This multivariate momentary evaluation scheme is a generalization of the fast multipole method in which calculations with far field expansions are replaced by calculations involving moments of the data. The primary advantage of this new algorithm is that it is highly adaptive to changes in Phi.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2000
Accession Number
ADP011971

Entities

People

  • E. Chacko
  • R. K. Beatson

Organizations

  • University of Canterbury

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Convolution
  • Dynamic Range
  • Equations
  • Far Field
  • Geometry
  • Mathematics
  • Near Field
  • Notation
  • Permutations
  • Polynomials
  • Symmetry
  • Technical Information Centers
  • Test And Evaluation
  • Two Dimensional

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Analytical Mechanics
  • Calculus or Mathematical Analysis