Abstract
A new approach to the rational Zolotarev problem in the complex plane is presented. This minimization problem for rational functions arises from the determination of optimal parameters for the ADI iterative method applied to nonsymmetric systems of linear equations. Based on a generalization due to Walsh of the Fejér points which are well known in connection to polynomial interpolation in the complex plane, we are able to construct rational functions which are almost optimal for the rational Zolotarev problem in an asymptotic sense. For the construction of these Fejér-Walsh points, we make use of the Schwarz-Christoffel mapping for doubly-connected polygonal regions due to Akhiezer and its recent implementation by Däppen. A numerical example illustrates the usefulness of the Fejér-Walsh points as ADI parameters.
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