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Fast algorithms for spherical harmonic expansions

delete2006-01-01
delete79
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OA
AI
R
Rokhlin, V *
M
Mark Tygert
DOI：10.1137/050623073delete
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Abstract

Abstract

En 中文
An algorithm is introduced for the rapid evaluation at appropriately chosen nodes on the two-dimensional sphere S-2 in R-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-2 ( known as the forward spherical harmonic transform). The procedure is numerically stable and requires an amount of CPU time proportional to N-2( logN) log( 1/epsilon), where N-2 is the number of nodes in the discretization of S-2, and e is the precision of computations. The performance of the algorithm is illustrated via several numerical examples.
Keywords:
spherical harmonics
fast algorithms
expansions

Journal

SIAM Journal on Scientific Computing cover
SIAM Journal on Scientific Computing
IF:
2.6
Papers:
5.1K
Citations:
1.8W

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No organization information available