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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
MathSciNet review: 528051
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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.

References [Enhancements On Off] (What's this?)

  • [1] J. W. COOLEY & J. W. TUKEY, "An algorithm for the machine calculation of complex Fourier series," Math. Comp., v. 19, 1965, pp. 297-301. MR 0178586 (31:2843)
  • [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. & ROBERT G. VOIGT, "The solution of tridiagonal linear systems on the CDC STAR-100 computer," ACM Trans. Math. Software, v. 1, 1975, pp. 308-329. MR 0388843 (52:9677)
  • [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 using base 8 iterations," Math. Comp., v. 22, 1968, pp. 275-279. MR 0226899 (37:2485)

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Keywords: Fast Fourier Transform, parallel computation
Article copyright: © Copyright 1979 American Mathematical Society

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