Fehlerabschätzung für die numerische Differentiation analytischer Funktionen durch Quadratur

Summary Numerical treatment of the integral in Cauchy's integral formula produces approximations for the derivatives of an analytic functionf; this fact has already been utilized byLyness andMoler 3, 4]. In the present paper this idea is investigated especially in view of the accuracy of these formulas regarded as quadrature formulas. Since the integration can be reduced to the integration of a periodic analytic function, it is possible to continue the considerations ofDavis 2] in order to find bounds for the error of the differentiation rules. For the application of these bounds one essentially needs estimations of the maximum off on a circle inside of its region of analyticity. Examples show the practical use of the bounds.

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Meinem verehrten LehrerH. Görtler zur Vollendung seines 60. Lebensjahres gewidmet