Error analysis for Fourier series evaluation
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.
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C. W. Clenshaw, "A note on the summation of Chebyshev series," MTAC, v. 9, 1955, pp. 118-120. MR 17, 194.
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.
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