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Uniform Approximations for Transcendental Functions

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Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2667))

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Abstract

A heuristic method to construct uniform approximations to analytic transcendental functions is developed as a generalization of the Hermite-Padé interpolation to infinite intervals. The resulting uniform approximants are built from elementary functions using known series and asymptotic expansions of the given transcendental function. In one case (Lambert’s W function) we obtained a uniform approximation valid in the entire complex plane. Several examples of the application of this method to selected transcendental functions are given.

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References

  1. J. von zur Gathen and J. Gerhard, Modern Computer Algebra, Cambridge University Press, 1999.

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  2. M. Abramowitz and I. Stegun, Handbook of special functions, National Bureau of Standards, 1964.

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Author information

Authors and Affiliations

  1. Department of Physics, Ludwig-Maximilians University, Theresienstr. 37, 80333, Munich, Germany

    Serge Winitzki

Authors
  1. Serge Winitzki
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Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA

    Vipin Kumar

  2. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  3. Heuchera Technologies Inc., 122 9251-8 Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  4. Département d’informatique et de recherche opérationelle, Université de Montréal, Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

  5. Department of Computer Science and Engineering, University of Minessota, MN, 55455, USA

    Vipin Kumar

  6. The Queen’s University of Belfast, School of Computer Science, Belfast BT7 1NN, Northern Ireland, UK

    Chih Jeng Kenneth Tan

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© 2003 Springer-Verlag Berlin Heidelberg

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Winitzki, S. (2003). Uniform Approximations for Transcendental Functions. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44839-X_82

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  • DOI: https://doi.org/10.1007/3-540-44839-X_82

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40155-1

  • Online ISBN: 978-3-540-44839-6

  • eBook Packages: Springer Book Archive

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