Segeth, Karel Roundoff errors in the fast computation of discrete convolutions. (English) Zbl 0474.65025 Apl. Mat. 26, 241-262 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Document MSC: 65F30 Other matrix algorithms (MSC2010) 65T40 Numerical methods for trigonometric approximation and interpolation 42A15 Trigonometric interpolation Keywords:discrete convolution; fast Fourier transform; analysis of the roundoff errors; stochastic model × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] R. Alt: Error propagation in Fourier transforms. Math. Comput. Simulation 20 (1978), 37-43. · Zbl 0386.65057 · doi:10.1016/0378-4754(78)90052-6 [2] J. W. Cooley J. W. Tukey: An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19 (1965), 297-301. · Zbl 0127.09002 · doi:10.2307/2003354 [3] P. J. Davis P. Rabinowitz: Methods of Numerical Integration. Academic Press, New York 1975. · Zbl 0304.65016 [4] R. W. Hamming: Numerical Methods for Scientists and Engineers. McGraw-Hill, New York 1962. · Zbl 0952.65500 [5] D. R. Hartree: Note on systematic roundoff errors in numerical integration. J. Res. Nat. Bur. Standards 42 (1949), 62. [6] H. D. Helms: Fast Fourier transform method of computing difference equations and simulating filters. IEEE Trans. Audio Electroacoust. AU-15 (1967), 85-90. · doi:10.1109/TAU.1967.1161905 [7] P. Henrici: Elements of Numerical Analysis. Wiley, New York 1964. · Zbl 0149.10901 [8] H. D. Huskey: On the precision of a certain procedure of numerical integration. J. Res. Nat. Bur. Standards 42 (1949), 57-62. · doi:10.6028/jres.042.005 [9] L. Jolley: Summation of Series. Chapman and Hall, London 1925. · Zbl 0101.28602 [10] T. Kaneko B. Liu: Accumulation of round-off error in fast Fourier transforms. J. Assoc. Comput. Mach. 17 (1970), 637-654. · Zbl 0218.65037 · doi:10.1145/321607.321613 [11] T. Kaneko B. Liu: On local roundoff errors in floating-point arithmetic. J. Assoc. Comput. Mach. 20 (1973), 391-398. · Zbl 0265.65026 · doi:10.1145/321765.321771 [12] G. U. Ramos: Roundoff error analysis of the fast Fourier transform. Math. Comp. 25 (1971), 757-768., · Zbl 0227.65068 · doi:10.2307/2004342 [13] P. H. Sterbenz: Floating-Point Computation. Prentics-Hall, Englewood Cliffs, N. J., 1974. [14] System/360 Scientific Subroutine Package. IBM Corporation, White Plains, N. Y., 1910. [15] T. Thong B. Liu: Accumulation of roundoff errors in floating point FFT. IEEE Trans. Circuits and Systems 24 (1977), 132-143. · Zbl 0364.65114 · doi:10.1109/TCS.1977.1084316 [16] T. Thong B. Liu: Floating point fast Fourier transform computation using double precision floating point accumulators. ACM Trans. Math. Software 3 (1977), 54-59. · Zbl 0349.65073 · doi:10.1145/355719.355723 [17] J. H. Wilkinson: Rounding Errors in Algebraic Processes. HMSO, London 1963. · Zbl 1041.65502 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.