Modified Newton's method with third-order convergence and multiple roots
type: Item
instance of: scholarly article
title: Modified Newton's method with third-order convergence and multiple roots
zbMATH Open document ID: 1030.65044
DOI: 10.1016/S0377-0427(02)00920-2
author: E. Sormani
author: M. Frontini
published in: Journal of Computational and Applied Mathematics
publication date: 2003-08-07T00:00:00Z
review text: Some modified Newton methods, with order of convergence three in the case of simple roots, obtained by using interpolatory quadrature formula and not requiring the second or higher derivatives of the function, are studied in the case of multiple roots. A typical result (Theorem 3) reads as follows: If \(\xi \) is a root of \(f(x)\) with multiplicity \(p>1\) (\(f(\xi)=0,\;f^{\prime }(\xi)=0,\dots ,f^{(p)}(\xi)\neq 0\)) then the modified Newton method obtained by using a quadrature formula of order at least \(p-1\) and using the corrected Newton's method has order of convergence two.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 1961625
zbMATH Keywords: modified Newton method
zbMATH Keywords: interpolatory quadrature formula
zbMATH Keywords: order of convergence
zbMATH Keywords: multiple root
reviewed by: Vasile Berinde
MaRDI profile type: Publication
cites work: Q3702408
cites work: Some variant of Newton's method with third-order convergence.
cites work: Q4354453
cites work: A variant of Newton's method with accelerated third-order convergence
description: scientific article; zbMATH DE number 1961625