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On the complexity of extending the convergence domain of Newton’s method under the weak majorant condition

Part of: Numerical methods in calculus of variations and optimal control

Published online by Cambridge University Press:  01 March 2024

Ioannis K. Argyros Open the ORCID record for Ioannis K. Argyros [Opens in a new window]  and
Santhosh George Open the ORCID record for Santhosh George [Opens in a new window]
Ioannis K. Argyros
Affiliation:
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, United States e-mail: iargyros@cameron.edu
Santhosh George*
Affiliation:
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575 025, India
*
e-mail: sgeorge@nitk.edu.in
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Abstract

The local analysis of convergence for Newton’s method has been extensively studied by numerous researchers under a plethora of sufficient conditions. However, the complexity of extending the convergence domain requires very general conditions such as the ones depending on the majorant principle in order to include as large classes of operators as possible. In the present article, such an analysis is developed under the weak majorant condition. The new results extend earlier ones using similar information. Finally, the numerical examples complement the theory.

Keywords

Newton’s methodsweak majorant conditionBanach spaceconvergence domain

MSC classification

Primary: 65K15: Numerical methods for variational inequalities and related problems 90C30: Nonlinear programming 49M15: Newton-type methods
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 15
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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