Error bounds for Newton's iterates derived from the Kantorovich theorem (Q1059985)

This paper shows that the upper and lower bounds of the errors in the Newton iterates recently obtained by \textit{F. Potra} and \textit{V. Pták} [ibid. 34, 63-72 (1980; Zbl 0434.65034)] and \textit{G. Miel} [Computing 27, 237-244 (1981; Zbl 0451.65042)] follow immediately from the Kantorovich theorem, the Kantorovich recurrence relations and Gragg-Tapia's technique. It is also shown that the upper and lower bounds of Miel are sharper than those of Potra-Pták.