Computing the fast Fourier transform on a vector computer

Authors:
David G. Korn and Jules J. Lambiotte

Journal:
Math. Comp. **33** (1979), 977-992

MSC:
Primary 65T05; Secondary 68C25

DOI:
https://doi.org/10.1090/S0025-5718-1979-0528051-4

MathSciNet review:
528051

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Abstract | References | Similar Articles | Additional Information

Abstract: Two algorithms are presented for performing a Fast Fourier Transform on a vector computer and are compared on the Control Data Corporation STAR-100. The relative merits of the two algorithms are shown to depend upon whether only a few or many independent transforms are desired.

A theorem is proved which shows that a set of independent transforms can be computed by performing a partial transformation on a single vector. The results of this theorem also apply to nonvector machines and have reduced the average time per transform by a factor of two on the CDC 6600 computer.

**[1]**James W. Cooley and John W. Tukey,*An algorithm for the machine calculation of complex Fourier series*, Math. Comp.**19**(1965), 297–301. MR**178586**, https://doi.org/10.1090/S0025-5718-1965-0178586-1**[2]**M. C. PEASE, "An adaptation of the fast Fourier transform for parallel processing,"*J. Assoc. Comput. Mach.*, v. 15, 1968, pp. 253-264.**[3]**Jules J. Lambiotte Jr. and Robert G. Voigt,*The solution of tridiagonal linear systems on the CDC STAR-100 computer*, ACM Trans. Math. Software**1**(1975), no. 4, 308–329. MR**388843**, https://doi.org/10.1145/355656.355658**[4]**W. T. COCHRAN ET AL., "What is the fast Fourier transform?,"*IEEE Trans. Audio Electroacoustics*, v. Au-15, 1967, pp. 45-55.**[5]**G. D. Bergland,*A fast Fourier transform algorithm using base 8 iterations*, Math. Comp.**22**(1968), 275–279. MR**226899**, https://doi.org/10.1090/S0025-5718-1968-0226899-X

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0528051-4

Keywords:
Fast Fourier Transform,
parallel computation

Article copyright:
© Copyright 1979
American Mathematical Society