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Zbl 0952.65027
Wachspress, E.L.
Evaluating elliptic functions and their inverses. (English)
[J] Comput. Math. Appl. 39, No.3-4, 131-136 (2000). ISSN 0898-1221

Summary: {\it D. G. Vyridis}, {\it S. D. Panteliou} and {\it I. N. Katz} [ibid. 37, No. 2, 21-26 (199; Zbl 0942.65019)] described an inverse interpolation scheme for estimating inverse Jacobian elliptic functions in an environment like MATLAB where direct but not inverse evaluation is available. Here, an easily programmed alternative based on the standard arithmetic-geometric-mean tabloid is developed. A novel recursion eliminates need for evaluating tangents and inverse tangents at intermediate steps in the algorithm. A similar algorithm is developed for evaluation of elliptic functions when given argument and modulus. The latter seems less beneficial, especially when standard software evaluation is available. Numerical results indicate robustness and high accuracy.

MSC 2000:: *65D20 Computation of special functions
33E05 Elliptic functions and integrals

Keywords: numerical results; inverse interpolation scheme; inverse Jacobian elliptic functions; algorithm

Citations: Zbl 0942.65019

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