A construction procedure of iterative methods with cubical convergence
type: Item
instance of: scholarly article
title: A construction procedure of iterative methods with cubical convergence
zbMATH Open document ID: 0879.65035
DOI: 10.1016/S0096-3003(96)00134-8
published in: Applied Mathematics and Computation
publication date: 1998-01-22T00:00:00Z
review text: Nonlinear operator equations in a Banach space, their solution by means of a parameter-based continuation method, and a Kantorovich-type convergence analysis for it are considered. The authors design new iterative methods based on a convex combination of the operators describing the well known third-order Chebyshev method and convergence acceleration of Newton's method. With the convergence result for this family of methods, an error estimate is given, too. The article is completed with examples and numerical tests.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 1062206
zbMATH Keywords: numerical examples
zbMATH Keywords: nonlinear operator equations
zbMATH Keywords: Banach space
zbMATH Keywords: continuation method
zbMATH Keywords: Kantorovich-type convergence analysis
zbMATH Keywords: iterative methods
zbMATH Keywords: Chebyshev method
zbMATH Keywords: convergence acceleration of Newton's method
zbMATH Keywords: error estimate
author: J. A. Ezquerro
author: José Manuel Gutiérrez Jimenez
author: M. A. Hernández
reviewed by: Etienne Emmrich
MaRDI profile type: Publication
cites work: Q4002082
cites work: Q5652137
cites work: Accessibility Of Solutions By Newton's Method
cites work: Results on the Chebyshev method in banach spaces
cites work: Recurrence relations for rational cubic methods. II: The Chebyshev method
cites work: Standard kantorovich theorem of the chebyshev method on complex plane
cites work: A local convergence theorem for the super-Halley method in a Banach space
cites work: Q4304466
cites work: A family of chebyshev-halley type methods
cites work: Q3943431
cites work: A Unified Convergence Theory for a Class of Iterative Processes
cites work: Q5728750
cites work: On Newton's method and nondiscrete mathematical induction
cites work: On the method of tangent hyperbolas in Banach spaces
cites work: Q4060241
cites work: Quadratic equations in Banach spaces
description: scientific article; zbMATH DE number 1062206