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Mathematics of Computation

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Rational Chebyshev approximations for the error function


Author: W. J. Cody
Journal: Math. Comp. 23 (1969), 631-637
MSC: Primary 65.25
DOI: https://doi.org/10.1090/S0025-5718-1969-0247736-4
MathSciNet review: 0247736
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Abstract: This note presents nearly-best rational approximations for the functions erf $ (x)$ and erfc $ (x)$, with maximal relative errors ranging down to between $ 6 \times {10^{ - 19}}$ and $ 3 \times {10^{ - 20}}$.


References [Enhancements On Off] (What's this?)

  • [1] J. F. Hart, et al., Computer Approximations, Siam Series in Appl. Math., Wiley, New York, 1968.
  • [2] C. Hastings, Jr., Approximations for Digital Computers, Princeton Univ. Press, Princeton, N. J., 1955. MR 16, 963. MR 0068915 (16:963e)
  • [3] C. W. Clenshaw, Chebyshev Series for Mathematical Functions, National Physical Lab. Math. Tables, vol. 5, H.M.S.O., London, 1962. MR 26 #362.
  • [4] W. J. Cody, W. Fraser & J. F. Hart, "Rational Chebyshev approximations using linear equations," Numer. Math., v. 12, 1968, pp. 242-251. MR 1553964

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1969-0247736-4
Article copyright: © Copyright 1969 American Mathematical Society

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