A 3D fast Fourier transform method with a linear-programming-derived power spectrum simulates CMB maps on partial-sky patches, with operation-count scaling suggesting speed advantages over HEALPix for some survey sizes.
Fast algorithms for spherical harmonic expansions, III
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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.
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Simulating Partial Sky Cosmic Microwave Background Maps with 3D Fast Fourier Transforms
A 3D fast Fourier transform method with a linear-programming-derived power spectrum simulates CMB maps on partial-sky patches, with operation-count scaling suggesting speed advantages over HEALPix for some survey sizes.