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We describe an efficient algorithm for calculating Fast Fourier
Transforms on matrices of arbitrarily high dimension using the
vector-radix method when the problem size is out-of-core (i.e.,
when the size of the data set is larger than the total available
memory of the system). The algorithm takes advantage of multiple
processors when they are present, but it is also efficient on single-processor
systems. Our work is an extension of work done by Lauren Baptist in
[Bapt99], which applied the vector-radix method to 2-dimensional
To determine the effectiveness of the algorithm, we present empirical results as well as an analysis of the I/O, communication, and computational complexity. We perform the empirical tests on a DEC 2100 server and on a cluster of Pentium-based Linux workstations. We compare our results with the traditional dimensional method of calculating multidimensional FFTs, and show that as the number of dimensions increases, the vector-radix-based algorithm becomes increasingly effective relative to the dimensional method.
In order to calculate the complexity of the algorithm, it was necessary to develop a method for analyzing the interprocessor communication costs of the BMMC data-permutation algorithm (presented in [CSW98]) used by our FFT algorithms. We present this analysis method and show how it was derived.
Masters Thesis. Advisor: Tom Cormen.
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
Or copy and paste:
Michael F. Ringenburg, "Applying the Vector Radix Method to Multidimensional, Multiprocessor, Out-of-Core Fast Fourier Transforms." Dartmouth Computer Science Technical Report TR2001-388, March 2001.
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