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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.

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Evaluation of Fourier integrals using $B$-splines
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by M. Lax and G. P. Agrawal PDF
Math. Comp. 39 (1982), 535-548 Request permission

Corrigendum: Math. Comp. 43 (1984), 347.
Corrigendum: Math. Comp. 43 (1984), 347.


Finite Fourier integrals of functions possessing jumps in value, in the first or in the second derivative, are shown to be evaluated more efficiently, and more accurately, using a continuous Fourier transform (CFT) method than the discrete transform method used by the fast Fourier transform (FFT) algorithm. A B-spline fit is made to the input function, and the Fourier transform of the set of B-splines is performed analytically for a possibly nonuniform mesh. Several applications of the CFT method are made to compare its performance with the FFT method. The use of a 256-point FFT yields errors of order ${10^{ - 2}}$, whereas the same information used by the CFT algorithm yields errors of order ${10^{ - 7}}$—the machine accuracy available in single precision. Comparable accuracy is obtainable from the FFT over the limited original domain if more than 20,000 points are used.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 535-548
  • MSC: Primary 65D30; Secondary 42A15, 65R10
  • DOI:
  • MathSciNet review: 669645