A convergence theorem for Newton-like methods under generalized Chen- Yamamoto-type assumptions
type: Item
instance of: scholarly article
title: A convergence theorem for Newton-like methods under generalized Chen- Yamamoto-type assumptions
zbMATH Open document ID: 0796.65077
DOI: 10.1016/0096-3003(94)90144-9
author: Ioannis Konstantinos Argyros
published in: Applied Mathematics and Computation
publication date: 1994-10-17T00:00:00Z
review text: The author provides sufficient conditions for the convergence of a Newton-like method to a locally unique solution of a nonlinear operator equation with a nondifferentiable term in a Banach space setting. He assumes the existence of real-valued functions of two variables that are upper bounds on the governing operator. Using a majorant method, the author proves that the sequence generated by the Newton-like method is well-defined and converges to a solution of the above-mentioned equation. An error estimate is given.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 554117
zbMATH Keywords: convergence
zbMATH Keywords: Newton-like method
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: Banach space
zbMATH Keywords: majorant method
zbMATH Keywords: error estimate
reviewed by: Yu Wenhuan
MaRDI profile type: Publication
full work available at URL: 0096-3003(94)90144-9
OpenAlex ID: W2033581615
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description: scientific article; zbMATH DE number 554117