Error bounds for Newton's iterates derived from the Kantorovich theorem
type: Item
instance of: scholarly article
title: Error bounds for Newton's iterates derived from the Kantorovich theorem
zbMATH Open document ID: 0567.65027
DOI: 10.1007/BF01389444
author: Tetsuro Yamamoto
published in: Numerische Mathematik
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133060
review text: 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.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65J15
zbMATH DE Number: 3905746
zbMATH Keywords: error bounds
zbMATH Keywords: Potra-Ptak's bounds
zbMATH Keywords: Miel's bounds
zbMATH Keywords: upper and lower bounds
zbMATH Keywords: Newton iterates
zbMATH Keywords: Kantorovich theorem
zbMATH Keywords: Kantorovich recurrence relations
zbMATH Keywords: Gragg-Tapia's technique
MaRDI profile type: Publication
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OpenAlex ID: W2071095292
description: scientific article; zbMATH DE number 3905746