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We extend the Weierstrass-Kerner method by applying the Chebychev method tothe function F that Kerner has used to show that the formula of Weierstrassactually is the Newton method applied to that F. The resulting method isalready known but we want to present the process in one go and in a detailedway.

\"Uber die Anwendung des Tschebyschew-Verfahrens zum Ausbau des Weierstra{\ss}-Kerner-Verfahrens