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Fast algorithms for spherical harmonic expansions
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DOI：10.1137/050623073.png)
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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.
Keyword:
spherical harmonics
fast algorithms
expansions
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2.6
论文数:
5.1K
被引数:
1.8W
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