Error bounds for Newton's iterates derived from the Kantorovich theorem
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.
scientific article; zbMATH DE number 3905746