The Future Fast Fourier Transform?

It seems likely that improvements in arithmetic speed will continue to outpace advances in communication bandwidth. Furthermore, as more and more problems are working on huge datasets, it is becoming increasingly likely that data will be distributed across many processors because one processor does not have sufficient storage capacity. For these reasons, we propose that an inexact DFT such as an approximate matrix-vector approach based on singular values or a variation of the Dutt–Rokhlin fast-multipole-based algorithm may outperform any exact parallel FFT. The speedup may be as large as a factor of three in situations where FFT run time is dominated by communication. For the multipole idea we further propose that a method of “virtual charges” may improve accuracy, and we provide an analysis of the singular values that are needed for the approximate matrix-vector approaches. Key words. parallel Fourier transforms, fast multipole method AMS subject classifications. 65T20, 65Y05, ...

• Type: Conference
• Year: 1997
• Where: PPSC
• Authors: Alan Edelman, Peter McCorquodale, Sivan Toledo
• Keywords: Approximate Matrix-vector, Approximate Matrix-vector Approach, PPSC 1997, PPSC 2001, Singular Values