Über die Konvergenzordnung des Intervall-Newton-Verfahrens. (On the order of convergence of the interval-Newton-method) (Q1092616)

It is well known that the classical Newton method is cubically convergent to a simple zero if the second derivative vanishes at the zero. We first show that this property does not hold for the interval-Newton-method. If, however, the interval arithmetic evaluation of the derivative in this method is replaced by the mean-value form or by the centered form, respectively, then the method is again cubically convergent.