Numerical experiments with algorithms for the ADI and Zolotarev coefficients

Abstract

In this paper, we present numerical experiments comparing the algorithms for computing the ADI and Zolotarev coefficients which involve Jacobi elliptic functions and the complete elliptic integral. We show that in some cases the algorithms, which use the standard MATLAB functions for computing the Jacobi elliptic functions and the complete elliptic integral, are less accurate than the algorithm of Zie¸tak, which can be applied when the number of coefficients is a power of 2. The algorithm of Zie¸tak is also competitive with the algorithms of Wachspress and Kennedy.