How to Increase the Accessibility of Newton's Method for Operators With Center-Lipschitz Continuous First Derivative. (17th February 2022)

• Record Type: Journal Article
• Authors: Ezquerro, J. A.; Hernández-Verón, M. A.; Magreñán, Á. A.
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 3(2022)
• Page Start: 350
• Page End: 363
• Publication Date: 2022-02-17
• Subjects: the modified Newton method -- Newton's method -- hybrid method -- semilocal convergence -- majorizing sequence -- accessibility -- boundary value problem; 65H10 -- 65J15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2030352
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: As accessibility of Newton's method is very restrictive under a center-Lipschitz condition for the first derivative of the operator involved, we construct a hybrid iterative method to increase the accessibility of the method, where the modified Newton method is used to predict a good starting approximation for Newton's method. A boundary value problem illustrates this study.