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Evaluating elliptic functions and their inverses. (English) Zbl 0952.65027
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.

65D20Computation of special functions, construction of tables
33E05Elliptic functions and integrals
Full Text: DOI
[1] Vyridis, D. G.; Panteliou, S. D.; Katz, I. N.: An inverse convergence approach for arguments of Jacobian elliptic functions. Computers math. Applic. 37, No. 2, 21-26 (1999) · Zbl 0942.65019
[2] Abramowitz, M.; Stegun, I. A.: Handbook of mathematical functions. (1964) · Zbl 0171.38503
[3] Wachspress, E. L.: The ADI model problem. (1995) · Zbl 1277.65022