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Computation of Interval Bounds for Weierstrass’ Elliptic Function ℘(z)

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Validation Numerics

Part of the book series: Computing Supplementum ((COMPUTING,volume 9))

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Abstract

Computation of Interval Bounds for Weierstrass’ Elliptic Function ℘(z. A method to enclose the values of Weierstrass’ elliptic function ℘(z) = ℘(z|g 2,g 3) for arbitrary complex invariants g 2,g 3 or arbitrary given zeros of the characteristic polynomial (arbitrary period lattices) is presented. The function is approximated by its truncated Laurent series at zero. An error bound is derived for the remainder term. If necessary, the periodicity of ℘, the homogeneity relations and the addition formulas are used to perform the reduction of the argument and the corresponding adaptation of the result.

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Karlsruhe, D-W-7500, Karlsruhe 1, Federal Republic of Germany

    Walter Krämer

  2. Institut für Industrielle Bauproduktion, Universität Karlsruhe, D-W-7500, Karlsruhe 1, Federal Republic of Germany

    Bertram Barth

Authors
  1. Walter Krämer
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  2. Bertram Barth
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität Innsbruck, Austria

    R. Albrecht

  2. Institut für Angewandte Mathematik, Universität Karlsruhe, Federal Republic of Germany

    G. Alefeld

  3. Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Austria

    H. J. Stetter

Additional information

Dedicated to Professor U. Kulisch on the occasion of his 60th birthday

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© 1993 Springer-Verlag

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Krämer, W., Barth, B. (1993). Computation of Interval Bounds for Weierstrass’ Elliptic Function ℘(z). In: Albrecht, R., Alefeld, G., Stetter, H.J. (eds) Validation Numerics. Computing Supplementum, vol 9. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6918-6_12

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  • DOI: https://doi.org/10.1007/978-3-7091-6918-6_12

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82451-1

  • Online ISBN: 978-3-7091-6918-6

  • eBook Packages: Springer Book Archive

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