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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Very high accuracy Chebyshev expansions for the basic trigonometric functions
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by J. L. Schonfelder PDF
Math. Comp. 34 (1980), 237-244 Request permission

Abstract:

Chebyshev expansion coefficients, accurate to forty decimal places, for the functions sine, cosine, and tangent, are tabulated. The methods used to generate the expansions are outlined and the ways in which accuracy of the tabulated coefficients were checked are noted.
References
  • C. W. Clenshaw, Chebyshev series for mathematical functions, National Physical Laboratory Mathematical Tables, Vol. 5, Her Majesty’s Stationery Office, London, 1962. Department of Scientific and Industrial Research. MR 0142793
  • Y. L. LUKE, The Special Functions and Their Approximations, Vols. 1, 2, Academic Press, New York, 1969. J. L. SCHONFELDER, "The production of special function routines for a multi-machine library," Software-Practical and Experience, vol. 6, 1976, pp. 71-82; "The production and testing of special function software in the NAG library" (Goos and Hartmanis, Eds.), Portability of Numerical Software, Lecture Notes in Computer Science, Vol. 57, Springer-Verlag, Berlin and New York, 1976. J. L. SCHONFELDER & J. T. THOMASON, "Applications support by direct language extension" (Gelenbe and Portier, Eds.), International Computing Symposium 1975, North-Holland, Amsterdam, 1975; "Arbitrary precision arithmetic in Algol 68," in Software—Practice and Experience, Vol. 9, No. 3, 1979, pp. 173-182.
  • J. L. Schonfelder, Chebyshev expansions for the error and related functions, Math. Comp. 32 (1978), no. 144, 1232–1240. MR 494846, DOI 10.1090/S0025-5718-1978-0494846-8
  • L. Fox and I. B. Parker, Chebyshev polynomials in numerical analysis, Oxford University Press, London-New York-Toronto, Ont., 1968. MR 0228149
  • J. L. SCHONFELDER, "Generation of high precision Chebyshev expansions." (In preparation.)
  • Yudell L. Luke, Algorithms for the computation of mathematical functions, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977. MR 0494840
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 34 (1980), 237-244
  • MSC: Primary 65D20
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0551302-5
  • MathSciNet review: 551302