Application of iterative processes of \(R\)-order at least three to operators with unbounded second derivative
type: Item
instance of: scholarly article
title: Application of iterative processes of \(R\)-order at least three to operators with unbounded second derivative
zbMATH Open document ID: 1115.65063
published in: Applied Mathematics and Computation
publication date: 2007-03-12T00:00:00Z
review text: The paper investigates the iterative solution of a nonlinear operator equation in a Banach space. The authors try to present in a unified form a lot of well-known iterative methods (Chebyshev method, Halley method, super-Halley method, Euler method, Ostrowski method) by introducing a new linear operator. Thus, a family of Newton-like methods that includes the methods mentioned above is obtained. A semilocal convergence result for this family is stated and proved. The assumptions required for the second and for the third Fréchet-derivative of the operator are weaker. The convergence result is applied for solving a boundary value problem for a second order nonlinear ordinary differential equation.
reviewed by: Iulian Coroian
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 65L10
zbMATH DE Number: 5132962
zbMATH Keywords: Banach spaces
zbMATH Keywords: Newton-like methods
zbMATH Keywords: semilocal convergence
zbMATH Keywords: Kantorovich type theorem
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: Chebyshev method
zbMATH Keywords: Halley method
zbMATH Keywords: Euler method
zbMATH Keywords: Ostrowski method
author: M. A. Hernández
author: Natalia Romero
MaRDI profile type: Publication
full work available at URL: j.amc.2006.07.081
OpenAlex ID: W2157478146
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DOI: 10.1016/J.AMC.2006.07.081
description: scientific article; zbMATH DE number 5132962