An Algorithm for the Rapid Evaluation of Special Function Transforms

Abstract

We introduce a fast algorithm for the numerical application to arbitrary vectors of several special function transforms. The algorithm requires O(n log(n)) operations to apply to an arbitrary vector any n n matrix such that the rank of any p q contiguous submatrix is bounded by a constant times pq/n. These rank bounds are proven here for the case of the Fourier-Bessel transform. Numerical experiments demonstrate a much wider applicability. The performance of the algorithm is illustrated via several numerical examples.

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Document Details

Document Type
Technical Report
Publication Date
Apr 15, 2008
Accession Number
ADA482145

Entities

People

  • Franco Woolfe
  • Michael O'Neil
  • Vladimir Rokhlin, Jr.

Organizations

  • Yale University

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Bessel Functions
  • Chebyshev Polynomials
  • Coefficients
  • Complex Numbers
  • Computations
  • Decomposition
  • Discrete Fourier Transforms
  • Gaussian Quadrature
  • Hierarchies
  • Integrals
  • Interpolation
  • Lepidoptera
  • Numbers
  • Numerical Analysis
  • Polynomials
  • Real Numbers

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra