Abstract
This article is a partial review of some old work and some new work. Its purpose is to connect up apparently different rules and methods. In particular, an attempt is made to put the Filon Luke rules, the Euler Expansion method, and the Fast Fourier Transform in proper relative perspective to one another.
The emphasis here is on the analytical properties of these rules, on how to classify them, and on how to arrange the calculations. There is no discussion of the relative merits of various rules and no error expressions are given.
This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under contract W-31-109-Eng-38.
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References
M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Nat. Bur. Standards Appl. Math. Series, 55, U.S. Government Printing Office, Washington, D.C., 1964; 3rd printing with corrections, 1965, MR 29#4914; MR 31 #1400.
G. Giunta and A. Murli, ‘Algorithm XXX: Lynco: To Calculate Fourier Coefficients’, ACM Trans, on Math. Soft., to appear in 1987.
J. N. Lyness, Computational Techniques Based on the Lanczos Representation,’ Math. Comp. 28 (1974) 81–123.
J. N. Lyness, Technical Memorandum 370, Applied Mathematics Division, Argonne National Laboratory, Argonne, IL, 1981.
J. N. Lyness, ‘The Calculation of Trigonometric Fourier Coefficients,’ Jour. Comp. Phys. 54, pp. 57–73, 1984.
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© 1987 D. Reidel Publishing Company
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Lyness, J.N. (1987). Some Quadrature Rules for Finite Trigonometric and Related Integrals. In: Keast, P., Fairweather, G. (eds) Numerical Integration. NATO ASI Series, vol 203. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3889-2_2
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DOI: https://doi.org/10.1007/978-94-009-3889-2_2
Publisher Name: Springer, Dordrecht
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