2008/02/12 by Lexing Ying, Sergey Fomel, Ying, Lexing +1
Computer Science · Physics and Astronomy · #65R10 #65T50 #Blind Source Separation Techniques #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Scientific Research and Discoveries
paper · pdf · doi:10.48550/arxiv.0802.1554
openalex publication_date 2008/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to decompose the summation domain of into simpler components in a multiscale way. Existing fast algorithms are then applied to each component to obtain optimal complexity. The algorithm in 1D is exact and takes O(Nlog2 N) steps. Our solution in 2D is an approximate but accurate algorithm that takes O(N2 log2 N) steps. In both cases, the complexities are almost linear in terms of the degree of freedom. We provide numerical results on several test examples.