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 | References | Similar Articles | Additional Information
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.
- [1] C. W. Clenshaw, A note on the summation of Chebyshev series, Math. Tables Aids Comput. 9 (1955), 118–120. MR 71856, https://doi.org/10.1090/S0025-5718-1955-0071856-0
- [2] W. M. Gentleman, An error analysis of Goertzel’s (Watt’s) method for computing Fourier coefficients, Comput. J. 12 (1969/70), 160–165. MR 243760, https://doi.org/10.1093/comjnl/12.2.160
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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
