Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Chebyshev expansions for the error and related functions
HTML articles powered by AMS MathViewer

by J. L. Schonfelder PDF
Math. Comp. 32 (1978), 1232-1240 Request permission

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
  • 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 (especially Vol. 2, pp. 323-324), Academic Press, New York, 1969.
  • Yudell L. Luke, Mathematical functions and their approximations, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0501762
  • Yudell L. Luke, Algorithms for the computation of mathematical functions, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977. MR 0494840
    • G. F. MILLER, Private communication. 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. 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. L. SCHONFELDER, "The production of special function routines for a multi-machine library," Software-Practice and Experience, vol. 6, 1976, pp. 71-82.
  • 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." (Manuscript in preparation.)
  • Handbook for automatic computation. Vol. II, Die Grundlehren der mathematischen Wissenschaften, Band 186, Springer-Verlag, New York-Heidelberg, 1971. Linear algebra; Compiled by J. H. Wilkinson and C. Reinsch. MR 0461856
    • 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
  • © Copyright 1978 American Mathematical Society
  • Journal: Math. Comp. 32 (1978), 1232-1240
  • MSC: Primary 65D20; Secondary 33A20
  • DOI: https://doi.org/10.1090/S0025-5718-1978-0494846-8
  • MathSciNet review: 0494846