A Divide-and-Conquer Algorithm for the Symmetric TridiagonalEigenproblem
SIAM Journal on Matrix Analysis and Applications
Efficient algorithms for computing a strong rank-revealing QR factorization
SIAM Journal on Scientific Computing
Generalized discrete spherical harmonic transforms
Journal of Computational Physics
Data Structures and Algorithms
Data Structures and Algorithms
On the Compression of Low Rank Matrices
SIAM Journal on Scientific Computing
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, II
Journal of Computational Physics
Sparse Fourier Transform via Butterfly Algorithm
SIAM Journal on Scientific Computing
A Butterfly Algorithm for Synthetic Aperture Radar Imaging
SIAM Journal on Imaging Sciences
Preparing scientific application software for exascale computing
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
| Hi-index | 31.45 |
We accelerate the computation of spherical harmonic transforms, using what is known as the butterfly scheme. This provides a convenient alternative to the approach taken in the second paper from this series on ''Fast algorithms for spherical harmonic expansions''. The requisite precomputations become manageable when organized as a ''depth-first traversal'' of the program's control-flow graph, rather than as the perhaps more natural ''breadth-first traversal'' that processes one-by-one each level of the multilevel procedure. We illustrate the results via several numerical examples.