Fast Algorithms for Spherical Harmonic Expansions

Abstract

An algorithm is introduced for the rapid evaluation at appropriately chosen nodes on the two-dimensional sphere S(exp 2) in R(exp 3) of functions specified by their spherical harmonic expansions (known as the inverse spherical harmonic transform), and for the evaluation of the coefficients in spherical harmonic expansions of functions specified by their values at appropriately chosen points on S(exp 2) (known as the forward spherical harmonic transform). The procedure is numerically stable and requires an amount of CPU time proportional to N(logN) log(1/epsilon), where N is the number of nodes in the discretization of S(exp 2), and epsilon is the precision of computations. The performance of the algorithm is illustrated via several numerical examples.

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Document Details

Document Type
Technical Report
Publication Date
Dec 17, 2004
Accession Number
ADA461342

Entities

People

  • Mark Tygert
  • Vladimir Rokhlin, Jr.

Organizations

  • Yale University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Chebyshev Polynomials
  • Computations
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Fast Fourier Transforms
  • Laguerre Functions
  • Legendre Functions
  • Mathematics
  • Numbers
  • Numerical Analysis
  • Partial Differential Equations
  • Polynomials
  • Real Numbers
  • Wave Functions

Readers

  • Approximation Theory.