On the semilocal convergence of efficient Chebyshev-secant-type methods
type: Item
instance of: scholarly article
title: On the semilocal convergence of efficient Chebyshev-secant-type methods
zbMATH Open document ID: 1215.65102
author: Ioannis Konstantinos Argyros
author: José Manuel Gutiérrez Jimenez
author: J. A. Ezquerro
author: M. A. Hernández
author: Saïd Hilout
published in: Journal of Computational and Applied Mathematics
publication date: 2011-04-13T00:00:00Z
review text: The authors introduce a three-step Chebyshev-secant-type method which is free of derivatives. Semilocal convergence analysis is presented and numerical tests are given.
reviewed by: János Karátson
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 49M15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 5877546
zbMATH Keywords: Banach space
zbMATH Keywords: Chebyshev's method
zbMATH Keywords: secant method
zbMATH Keywords: Newton's method
zbMATH Keywords: divided difference
zbMATH Keywords: recurrence relation
zbMATH Keywords: numerical examples
zbMATH Keywords: semilocal convergence
MaRDI profile type: Publication
full work available at URL: j.cam.2011.01.005
OpenAlex ID: W2087873880
cites work: An optimization of Chebyshev's method
cites work: A variant of Cauchy's method with accelerated fifth-order convergence.
cites work: Secant-like methods for solving nonlinear integral equations of the Hammerstein type
cites work: A multipoint method of third order
cites work: Q4401507
cites work: Q3702853
cites work: A new convergence theorem for the Jarratt method in Banach space
cites work: On the Newton-Kantorovich hypothesis for solving equations
cites work: A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
cites work: New sufficient convergence conditions for the secant method
cites work: Convergence and Applications of Newton-type Iterations
cites work: Solving a special case of conservative problems by secant-like methods
cites work: Q5652137
cites work: A convergence theorem for Newton-like methods in Banach spaces
cites work: On the weakening of the convergence of Newton's method using recurrent functions
cites work: Q5796557
cites work: A note on the Kantorovich theorem for Newton iteration
cites work: Q5588027
cites work: Untere Fehlerschranken für Regula-Falsi-Verfahren
cites work: Extended iterative methods for the solution of operator equations
cites work: Q3943431
cites work: Q5617234
DOI: 10.1016/J.CAM.2011.01.005
description: scientific article