# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
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.

##### MSC:
 65D20 Computation of special functions, construction of tables 33E05 Elliptic functions and integrals
Matlab
Full Text:
##### References:
 [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