Fast Algorithms for Spherical Harmonic Expansions
YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE
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An algorithm is introduced for the rapid evaluation at appropriately chosen nodes on the two-dimensional sphere Sexp 2 in Rexp 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 Sexp 2 known as the forward spherical harmonic transform. The procedure is numerically stable and requires an amount of CPU time proportional to NlogN log1epsilon, where N is the number of nodes in the discretization of Sexp 2, and epsilon is the precision of computations. The performance of the algorithm is illustrated via several numerical examples.
- Statistics and Probability
- Computer Programming and Software