Error Bounds for Newton's Iterates Derived from the Kantorovich Theorem

摘要

In this reprint, it is shown that the upper and lower bounds of the errors in the Newton iterates recently obtained by Potra-Ptak and Miel, with the use of nondiscrete induction and majorizing sequence, respectively, follow immediately from the Kantorovich theorem and the Kantorovich recurrence relations. It is also shown that the upper and lower bounds of Miel are finer than those of Potra-Ptak. (Author)