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Mathematics of Computation

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Error analysis for Fourier series evaluation


Author: A. C. R. Newbery
Journal: Math. Comp. 27 (1973), 639-644
MSC: Primary 65J05
DOI: https://doi.org/10.1090/S0025-5718-1973-0366072-X
MathSciNet review: 0366072
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Abstract: A floating-point error analysis is given for the standard recursive method of evaluating trigonometric polynomials. It is shown that, by introducing a phase-shift, one can hold the error growth down to an essentially linear function of the degree. Explicit computable error bounds are derived and numerically verified.


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

  • [1] C. W. Clenshaw, "A note on the summation of Chebyshev series," MTAC, v. 9, 1955, pp. 118-120. MR 17, 194. MR 0071856 (17:194e)
  • [2] W. M. Gentleman, "An error analysis of Goertzel's (Watt's) method for computing Fourier coefficients," Comput. J., v. 12, 1969/70, pp. 160-165. MR 39 #5081. MR 0243760 (39:5081)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0366072-X
Keywords: Error analysis, Fourier series
Article copyright: © Copyright 1973 American Mathematical Society

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