Error analysis for Fourier series evaluation

Newbery, A. C. R.

doi:10.1090/S0025-5718-1973-0366072-X

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)

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Error analysis for Fourier series evaluation
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by A. C. R. Newbery PDF

Math. Comp. 27 (1973), 639-644 Request permission

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

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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, DOI 10.1093/comjnl/12.2.160