A New Class of Analysis-Based Fast Transforms

Abstract

We introduce a new approach to the rapid numerical application to arbitrary vectors of certain types of linear operators. Inter alia, our scheme is applicable to many classical integral transforms, and to the expansions associated with most families of classical special functions; among the latter are Bessel functions, Legendre, Hermite, and Laguerre polynomials, Spherical Harmonics, Prolate Spheroidal Wave functions, and a number of others. In all these cases, the CPU time requirements of our algorithm are of the order O(n log n), where n is the size of the matrix to be applied. The performance of our algorithm is illustrated via a number of numerical examples.

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Document Details

Document Type
Technical Report
Publication Date
Aug 06, 2007
Accession Number
ADA471850

Entities

People

  • Michael O'Neil
  • Vladimir Rokhlin, Jr.

Organizations

  • Yale University

Tags

Communities of Interest

  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Bessel Functions
  • Chebyshev Polynomials
  • Computational Complexity
  • Differential Equations
  • Discrete Fourier Transforms
  • Equations
  • Fourier Analysis
  • Gaussian Quadrature
  • Integral Transforms
  • Integrals
  • Laguerre Functions
  • Numbers
  • Periodic Functions
  • Polynomials
  • Real Numbers
  • Wave Functions

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Parallel and Distributed Computing.