High order iterative methods for approximating square roots
type: Item
instance of: scholarly article
title: High order iterative methods for approximating square roots
zbMATH Open document ID: 0870.65039
DOI: 10.1007/BF01731991
author: Bahman Kalantari
author: Iraj Kalantari
published in: BIT
publication date: 1997-09-17T00:00:00Z
review text: The authors describe an iteration function \(g_m(x)\) with \(m\geq 2\) having the propriety that for any initial iterate \(x_0> \sqrt \alpha\), the sequence of fixed-point iteration \(x_{k+1} =g_m (x_k)\) converges monotonically to \(\sqrt \alpha\) having \(m\)-th order rate of convergence. This function generalizes Newton's and Halley's iteration functions.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 12Y05
zbMATH DE Number: 885561
zbMATH Keywords: square roots
zbMATH Keywords: iteration function
zbMATH Keywords: fixed-point iteration
zbMATH Keywords: convergence
zbMATH Keywords: Newton's and Halley's iteration functions
MaRDI profile type: Publication
cites work: Q3996272
cites work: A Type of Variation on Newton's Method
cites work: A basic family of iteration functions for polynomial root finding and its characterizations
cites work: Q3343091
cites work: Q5732060
description: scientific article; zbMATH DE number 885561