The midpoint method in Banach spaces and the Pták error estimates
type: Item
instance of: scholarly article
title: The midpoint method in Banach spaces and the Pták error estimates
zbMATH Open document ID: 0796.65076
DOI: 10.1016/0096-3003(94)90129-5
author: Ioannis Konstantinos Argyros
author: D. Chen
published in: Applied Mathematics and Computation
publication date: 1994-10-10T00:00:00Z
review text: The authors introduce a midpoint two-step method, which contains a Newton method and a modified Newton method in each iteration, to solve approximately a nonlinear operator equation in a Banach space setting. They give existence and uniqueness theorems as well as an error analysis by the majorant method, assuming the Fréchet derivative of the operator involved satisfies Pták-like estimates. For a special choice of the function involved their method is of order three as other well-known Newton methods of order three.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 566115
zbMATH Keywords: Pták error estimates
zbMATH Keywords: midpoint two-step method
zbMATH Keywords: Newton method
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: Banach space
zbMATH Keywords: error analysis
zbMATH Keywords: majorant method
reviewed by: Yu Wenhuan
MaRDI profile type: Publication
full work available at URL: 0096-3003(94)90129-5
OpenAlex ID: W2085648156
cites work: On the solution of equations with nondifferentiable and Ptak error estimates
cites work: Some notions of nonstationary multistep iteration processes
cites work: The midpoint method for solving nonlinear operator equations in Banach space
cites work: Convergence domains of certain iterative methods for solving nonlinear equations
cites work: Q5332416
cites work: Sharp error bounds for Newton's process
cites work: The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
description: scientific article; zbMATH DE number 566115