Evaluating elliptic functions and their inverses

In [1], the authors 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.