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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

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.


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