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SIAM Rev. 32, pp. 252-261 (10 pages)
The FFT as a Multigrid Algorithm
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Add to FacebookApart from the fact that they are both ingenious and remarkably efficient, there would appear to be little kinship between fast Fourier transform (FFT) algorithms and basic multigrid methods. The fast Fourier transform is a powerful direct method for computing the discrete Fourier transform (DFT) of a sequence of complex numbers, whereas multigrid methods are highly refined iterative methods that can be used to approximate the solution of systems of equations. However, on closer examination, there are features of both algorithms that suggest at least a conceptual similarity. This note is written in a heuristic spirit and is intended to offer a motivation for the FFT that allows it to be viewed as a multigrid process. The outcome of this exercise is certainly not a more efficient FFT algorithm. But hopefully, it will serve to demonstrate the way in which multilevel thinking can be used to interpret algorithms and it may lead the way to new algorithms.
© 1990 Society for Industrial and Applied Mathematics
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Received March 20, 1989
Accepted August 22, 1989
Accepted August 22, 1989
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