A Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem
SIAM Journal on Matrix Analysis and Applications
A Divide-and-Conquer Algorithm for the Symmetric TridiagonalEigenproblem
SIAM Journal on Matrix Analysis and Applications
A fast spherical filter with uniform resolution
Journal of Computational Physics
Journal of Computational Physics
Generalized discrete spherical harmonic transforms
Journal of Computational Physics
An Improved Fast Multipole Algorithm for Potential Fields on the Line
SIAM Journal on Numerical Analysis
A fast spherical harmonics transform algorithm
Mathematics of Computation
Fast spherical Fourier algorithms
Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Fast Algorithms for Spherical Harmonic Expansions
SIAM Journal on Scientific Computing
An Accelerated Kernel-Independent Fast Multipole Method in One Dimension
SIAM Journal on Scientific Computing
A Fast Algorithm for the Calculation of the Roots of Special Functions
SIAM Journal on Scientific Computing
Short Note: Fast algorithms for spherical harmonic expansions, III
Journal of Computational Physics
Sparse Legendre expansions via l1-minimization
Journal of Approximation Theory
Scale Invariant Feature Transform on the Sphere: Theory and Applications
International Journal of Computer Vision
Spherical harmonic transform with GPUs
Euro-Par'11 Proceedings of the 2011 international conference on Parallel Processing
Preparing scientific application software for exascale computing
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
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We provide an efficient algorithm for calculating, at appropriately chosen points on the two-dimensional surface of the unit sphere in R^3, the values of functions that are specified by their spherical harmonic expansions (a procedure known as the inverse spherical harmonic transform). We also provide an efficient algorithm for calculating the coefficients in the spherical harmonic expansions of functions that are specified by their values at these appropriately chosen points (a procedure known as the forward spherical harmonic transform). The algorithms are numerically stable, and, if the number of points in our standard tensor-product discretization of the surface of the sphere is proportional to l^2, then the algorithms have costs proportional to l^2ln(l) at any fixed precision of computations. Several numerical examples illustrate the performance of the algorithms.