Reliable Computation of Elliptic Functions

Wolfram Luther (Gerhard-Mercator-Universität -GH Duisburg, Fachbereich Mathematik, Germany)

Werner Otten (Gerhard-Mercator-Universität -GH Duisburg, Fachbereich Mathematik, Germany)

Abstract: In this note we present rapidly convergent algorithms depending on the method of arithmetic-geometric means (AGM) for the computation of Jacobian elliptic functions and Jacobi's Theta-function. In particular, we derive explicit a priori bounds for the error accumulation of the corresponding Landen transform.

Keywords: AGM-method, Elliptic functions, Landen transform, a priori rounding error estimation