×

Calculation of complex Fourier coefficients using natural splines. (English) Zbl 0485.65096

MSC:

65T40 Numerical methods for trigonometric approximation and interpolation
42A15 Trigonometric interpolation
65D07 Numerical computation using splines
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cooley, J. W., Tukey, J. W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput.19, 297–301 (1965). · Zbl 0127.09002 · doi:10.1090/S0025-5718-1965-0178586-1
[2] Dierckx, P., Piessens, R.: Calculation of Fourier coefficients of discrete functions using cubic splines. J. Comput. Appl. Math.3, 207–209 (1977). · Zbl 0368.65066 · doi:10.1016/S0377-0427(77)80010-1
[3] Einarsson, B.: Numerical calculation of Fourier integrals with cubic splines. B.I.T.8, 279–286 (1968). · Zbl 0187.10501
[4] Gautschi, W.: Attenuation factors in practical Fourier analysis. Numer. Math.18, 373–400 (1972). · Zbl 0231.65101 · doi:10.1007/BF01406676
[5] Golomb, M.: Approximation by periodic spline interpolants on uniform meshes. J. Approximation Theory1, 26–65 (1968). · Zbl 0185.30901 · doi:10.1016/0021-9045(68)90055-5
[6] Greville, T. N. E.: Introduction to spline functions. Theory and applications of spline functions (Greville, T. N. E., ed.), 1–35. New York: Academic Press 1969. · Zbl 0215.17601
[7] Lee, E. T. Y., Chang, Gau-Zu: On numerical evaluation of Fourier coefficients by splines. Bull. Inst. Math. Acad. Sinica4, 237–248 (1976). · Zbl 0359.65106
[8] Lyche, T., Schumaker, L. L.: Computation of smoothing and interpolating natural splines via local bases. SIAM J. Numer. Anal.10, 1027–1038 (1973). · Zbl 0268.65006 · doi:10.1137/0710085
[9] Lyche T., Schumaker, L. L.: ALGOL procedures for computing smoothing and interpolating natural splines. Report CNA-31, Center for Numerical Analysis, The University of Texas at Austin, 1973. · Zbl 0239.65015
[10] Marsden, M. J., Taylor, G. D.: Numerical evaluation of Fourier integrals. Numerische Methoden der Approximationstheorie, Band 1 (Collatz, L., Meinardus, G., eds.), pp. 61–76. Basel: Birkhäuser 1972. · Zbl 0249.65012
[11] Marti, J. T.: An algorithm recursively computing the exact Fourier coefficients ofB-splines with nonequidistant knots. J. Appl. Math. Phys.29, 301–305 (1978). · Zbl 0378.65066 · doi:10.1007/BF01601524
[12] Neuman, E.: Moments and Fourier transforms ofB-splines. J. Comput. Appl. Math.7, 51–62 (1981). · Zbl 0452.42006 · doi:10.1016/0771-050X(81)90008-5
[13] Riordan, J.: An introduction to combinatorial analysis. New York: Wiley 1958. · Zbl 0078.00805
[14] Scherer, K.: Über die Konvergenz von natürlichen interpolierenden Splines. Linear Operators and Approximation (Butzer, P. L., Kahane, J.-P., eds.), pp. 487–492. Basel: Birkhäuser 1972. · Zbl 0253.41008
[15] Silliman, S. D.: The numerical evaluation by splines of Fourier transform. J. Approximation Theory12, 32–51 (1974). · Zbl 0291.41024 · doi:10.1016/0021-9045(74)90056-2
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.