2020/04/23 by James Bremer, Chen Ze, Ze Chen +4 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Digital Filter Design and Implementation #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2004.11346
openalex publication_date 2020/04/23 · openalex created_date 2020/05/01 · arxiv created 2021/08/28 · arxiv updated 2021/08/31 · openalex updated_date 2026/07/28
We describe an algorithm for the application of the forward and inverse spherical harmonic transforms. It is based on a new method for rapidly computing the forward and inverse associated Legendre transforms by hierarchically applying the interpolative decomposition butterfly factorization (IDBF). Experimental evidence suggests that the total running time of our method -- including all necessary precomputations -- is O(N2 log3(N)), where N is the order of the transform. This is nearly asymptotically optimal. Moreover, unlike existing algorithms which are asymptotically optimal or nearly so, the constant in the running time of our algorithm is small enough to make it competitive with state-of-the-art O(N3) methods at relatively small values of N. Numerical results are provided to demonstrate the effectiveness and numerical stability of the new framework.