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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On computing the discrete Fourier transform
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by S. Winograd PDF
Math. Comp. 32 (1978), 175-199 Request permission

Abstract:

A new algorithm for computing the Discrete Fourier Transform is described. The algorithm is based on a recent result in complexity theory which enables us to derive efficient algorithms for convolution. These algorithms are then used to obtain the new Discrete Fourier Transform algorithm.
References
    S. WINOGRAD, "Some bilinear forms whose multiplicative complexity depends on the field of constants," to be published in Mathematical Systems Theory, Vol. 10.
  • 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, DOI 10.1090/S0025-5718-1965-0178586-1
  • C. M. FIDUCCIA & Y. ZALCSTEIN, Algebras Having Linear Multiplicative Complexities, Technical Report 46, Dept. of Computer Science, State University of New York, Stony Brook, August 1975.
  • A. L. Toom, The complexity of a scheme of functional elements simulating the multiplication of integers, Dokl. Akad. Nauk SSSR 150 (1963), 496–498 (Russian). MR 0156494
  • C. M. RADER, "Discrete Fourier transforms when the number of data samples is prime," Proc. IEEE, v. 5, no. 6, June 1968, pp. 1107-1108.
  • I. J. Good, The interaction algorithm and practical Fourier analysis, J. Roy. Statist. Soc. Ser. B 20 (1958), 361–372. MR 102888
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Math. Comp. 32 (1978), 175-199
  • MSC: Primary 68A10
  • DOI: https://doi.org/10.1090/S0025-5718-1978-0468306-4
  • MathSciNet review: 0468306