Recurrence relations for super-Halley's method with Hölder continuous second derivative in Banach spaces
type: Item
instance of: scholarly article
title: Recurrence relations for super-Halley's method with Hölder continuous second derivative in Banach spaces
zbMATH Open document ID: 1279.47088
author: M. Prashanth
author: D. K. Gupta
published in: Kodai Mathematical Journal
publication date: 2013-05-24T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.kmj/1364562724
review text: The semilocal convergence of a third order super-Halley's method for approximating a locally unique solution of the nonlinear operator equation \(F(x)=0\) in Banach space is discussed. Using a new family of recurrence relations, the authors prove the convergence and the R-order of the method, based on the assumption that the second Fréchet derivatives of the nonlinear operator is Hölder continuous. Numerical examples are used to illustrate the efficiency of the proposed algorithm.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65J15
zbMATH DE Number: 6165617
zbMATH Keywords: super-Halley's method
zbMATH Keywords: Hölder continuity condition
zbMATH Keywords: Fréchet derivative
zbMATH Keywords: nonlinear operator equations
reviewed by: Zhen Mei
MaRDI profile type: Publication
OpenAlex ID: W2011849819
DOI: 10.2996/KMJ/1364562724
description: scientific article; zbMATH DE number 6165617