A fast algorithm for particle simulations
Journal of Computational Physics
A fast algorithm for the evaluation of Legendre expansions
SIAM Journal on Scientific and Statistical Computing
Fast algorithms for polynomial interpolation, integration, and differentiation
SIAM Journal on Numerical Analysis
A fast transform for spherical harmonics
A fast transform for spherical harmonics
A fast spherical filter with uniform resolution
Journal of Computational Physics
FFTs for the 2-Sphere-Improvements and Variations
FFTs for the 2-Sphere-Improvements and Variations
Fast spherical Fourier algorithms
Journal of Computational and Applied Mathematics
Another preprocessing algorithm for generalized one-dimensional fast multipole method
Journal of Computational Physics
A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering
Journal of Computational Physics
Spectral radial basis functions for full sphere computations
Journal of Computational Physics
Fast algorithms for spherical harmonic expansions, II
Journal of Computational Physics
Algorithm 888: Spherical Harmonic Transform Algorithms
ACM Transactions on Mathematical Software (TOMS)
Toward an efficient triangle-based spherical harmonics representation of 3D objects
Computer Aided Geometric Design
Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
ACM Transactions on Mathematical Software (TOMS)
Spherical harmonic analysis and synthesis using FFT: Application to temporal gravity variation
Computers & Geosciences
Unified array manifold decomposition based on spherical harmonics and 2-D Fourier basis
IEEE Transactions on Signal Processing
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The spectral method with discrete spherical harmonics transform plays an important role in many applications. In spite of its advantages, the spherical harmonics transform has a drawback of high computational complexity, which is determined by that of the associated Legendre transform, and the direct computation requires time of O(N3) for cut-off frequency N. In this paper, we propose a fast approximate algorithm for the associated Legendre transform. Our algorithm evaluates the transform by means of polynomial interpolation accelerated by the Fast Multipole Method (FMM). The divide-and-conquer approach with split Legendre functions gives computational complexity O(N2 log N). Experimental results show that our algorithm is stable and is faster than the direct computation for N ≥ 511.