Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 

 

Chebyshev expansions for the error and related functions


Author: J. L. Schonfelder
Journal: Math. Comp. 32 (1978), 1232-1240
MSC: Primary 65D20; Secondary 33A20
MathSciNet review: 0494846
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: New 30 decimal place Chebyshev expansions, which can be used to obtain approximations up to that accuracy, for the error function and its complement are presented. Bilinear and biquadratic mappings of the independent variable have been employed, in one case to improve convergence and in the other to increase the basic approximation range. The practical effects of these mappings are discussed, and the method used to generate the tabulated expansions is outlined. The expansions here presented form the basis of the routines in the S15 chapter of the NAG library.


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

  • [1] C. W. Clenshaw, Chebyshev series for mathematical functions, National Physical Laboratory Mathematical Tables, Vol. 5. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London, 1962. MR 0142793
  • [2] Y. L. LUKE, The Special Functions and their Approximations, Vols. 1, 2 (especially Vol. 2, pp. 323-324), Academic Press, New York, 1969.
  • [Y] Yudell L. Luke, Mathematical functions and their approximations, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0501762
  • [Y] Yudell L. Luke, Algorithms for the computation of mathematical functions, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977. MR 0494840
  • [3] G. F. MILLER, Private communication.
  • [4] J. L. SCHONFELDER, "The NAG library and its special functions chapter," International Computing Symposium 1974 (A. Günther et al., Editors), North-Holland, Amsterdam; American Elsevier, New York, 1974.
  • [J] L. SCHONFELDER, "Special functions in the NAG library," Software for Numerical Mathematics (D. J. Evans, Editor), (Proc. Conf., 1973), Academic Press, London and New York, 1974, pp. 285-300.
  • [J] L. SCHONFELDER, "The production of special function routines for a multi-machine library," Software-Practice and Experience, vol. 6, 1976, pp. 71-82.
  • [5] L. Fox and I. B. Parker, Chebyshev polynomials in numerical analysis, Oxford University Press, London-New York-Toronto, Ont., 1968. MR 0228149
  • [6] J. L. SCHONFELDER, "Generation of high precision Chebyshev expansions." (Manuscript in preparation.)
  • [7] Handbook for automatic computation. Vol. II, Springer-Verlag, New York-Heidelberg, 1971. Linear algebra; Compiled by J. H. Wilkinson and C. Reinsch; Die Grundlehren der Mathematischen Wissenschaften, Band 186. MR 0461856
  • [8] J. L. SCHONFELDER & J. T. THOMASON, "Applications support by direct language extension--An arbitrary precision arithmetic facility in Algol 68," International Computing Symposium 1975 (Proc. Sympos., Antibes, 1975), E. Gelenbe and D. Potier (Editors), North-Holland, Amsterdam; American Elsevier, New York, 1975.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D20, 33A20

Retrieve articles in all journals with MSC: 65D20, 33A20


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1978-0494846-8
Keywords: Special function approximation, error functions, Chebyshev expansions
Article copyright: © Copyright 1978 American Mathematical Society