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Error propagation in Fourier transforms. (English) Zbl 0386.65057


MSC:

65T40 Numerical methods for trigonometric approximation and interpolation
65G50 Roundoff error
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42B05 Fourier series and coefficients in several variables
Full Text: DOI

References:

[1] Alt, R., Etude statistique de l’erreur numérique d’affectation sur un ordinateur d’arithméthique en bas quelconque, (I.P. Report no. 76-5 (Febr. 1976), University of Paris VI), (french)
[2] W.M. Gentleman and G. Sande, Fast Fourier Transform for Fun and Profit, Proc. AFIPS 1966, Fall Joint Comput. Conf., vol. 29 (Spartan Books, New York), 563-578.; W.M. Gentleman and G. Sande, Fast Fourier Transform for Fun and Profit, Proc. AFIPS 1966, Fall Joint Comput. Conf., vol. 29 (Spartan Books, New York), 563-578.
[3] Kaneko, T.; Liu, B., Accumulation of Round-off Error in Fast Fourier Transform, J. of Ass. Comp. Mach., 17, 637-654 (1970) · Zbl 0218.65037
[4] La Porte, M.; Vignes, J., Etude statistique des erreurs dans l’arithmétique des ordinateurs. Application au contrôle des résultats d’algorithmes, Numer. Math., 23, 63-72 (1974) · Zbl 0278.65043
[5] La Porte, M.; Vignes, J., Evaluation de l’incertitude sur la solution d’un système linéaire, Numer. Math., 24, 39-47 (1975) · Zbl 0288.65020
[6] Vignes, J.; La Porte, M., Error Analysis in Computing, Proceedings of IFIP Congress, 610-614 (August 1974), Stockholm · Zbl 0295.65035
[7] Weinstein, C. J., Roud-off Noise in Floating Point Fast Fourier Transform Computation, IEEE Trans. Audio and Electro Acoustics, 209-215 (1969), AU-17
[8] Wilkinson, J. H., Error Analysis of Floating Point Computation, J. Ass. Comp. Mach., 8, 281-330 (1961) · Zbl 0109.09005
[9] Wilkinson, J. H., Rounding Errors in Algebraic Processes (1963), Prentice Hall · Zbl 0868.65027
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