Regular Article: Computing Fourier Transforms and Convolutions on the 2-Sphere
Advances in Applied Mathematics
Generalized discrete spherical harmonic transforms
Journal of Computational Physics
Spherical harmonic transforms for discrete multiresolution applications
The Journal of Supercomputing
Optimization of computations in global geopotential field applications
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartII
Optimization of spherical harmonic transform computations
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
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Spherical Harmonic Transforms (SHTs) which are essentially Fourier transforms on the sphere are critical in global geopotential and related applications. Among the best known strategies for discrete SHTs are Chebychev quadratures and least squares. The numerical evaluation of the Legendre functions are especially challenging for very high degrees and orders which are required for advanced geocomputations. The computational aspects of SHTs and their inverses using both quadrature and least-squares estimation methods are discussed with special emphasis on numerical preconditioning that guarantees reliable results for degrees and orders up to 3800 in REAL*8 or double precision arithmetic. These numerical results of spherical harmonic synthesis and analysis using simulated spectral coefficients are new and especially important for a number of geodetic, geophysical and related applications with ground resolutions approaching 5 km.