A fast algorithm for particle simulations
Journal of Computational Physics
Discrete cosine transform: algorithms, advantages, applications
Discrete cosine transform: algorithms, advantages, applications
Fast Fourier transforms for nonequispaced data
SIAM Journal on Scientific Computing
Regular Article: Computing Fourier Transforms and Convolutions on the 2-Sphere
Advances in Applied Mathematics
Fast algorithms for polynomial interpolation, integration, and differentiation
SIAM Journal on Numerical Analysis
SIAM Journal on Computing
Fast algorithms for discrete polynomial transforms
Mathematics of Computation
A Multiresolution Approach to Regularization of Singular Operators and Fast Summation
SIAM Journal on Scientific Computing
A fast spherical harmonics transform algorithm
Mathematics of Computation
Efficiency and Stability Issues in the Numerical Computation of Fourier Transforms and Convolutions on the 2-Sphere
Nonuniform fast Fourier transforms using min-max interpolation
IEEE Transactions on Signal Processing
Fast algorithms for spherical harmonic expansions, II
Journal of Computational Physics
Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
ACM Transactions on Mathematical Software (TOMS)
International Journal of Computer Vision
Design and implementation of the system for remote voltage harmonic monitor
ICESS'04 Proceedings of the First international conference on Embedded Software and Systems
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Spherical Fourier series play an important role in many applications. A numerically stable fast transform analogous to the fast Fourier transform is of great interest. For a standard grid of O(N2) points on the sphere, a direct calculation has computational complexity of O(N4), but a simple separation of variables reduces the complexity to O(N3). Here we improve well-known fast algorithms for the discrete spherical Fourier transform with a computational complexity of O(N2 log2 N). Furthermore we present, for the first time, a fast algorithm for scattered data on the sphere. For arbitrary O(N2) points on the sphere, a direct calculation has a computational Complexity of O(N4), but we present an approximate algorithm with a computational complexity of O(N2 log2 N).