Kantorovich-Like Convergence Theorems for Newton's Method Using Restricted Convergence Domains. (17th February 2019)

• Record Type: Journal Article
• Authors: Argyros, Ioannis K.; George, Santhosh
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 3(2019)
• Page Start: 303
• Page End: 318
• Publication Date: 2019-02-17
• Subjects: Banach space -- Kantorovich hypothesis -- Newton's method -- restricted domains -- semi-local convergence; 47H17 -- 49M15 -- 49J53 -- 65G99; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1554582
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The convergence set for Newton's method is small in general using Lipschitz-type conditions. A center-Lipschitz-type condition is used to determine a subset of the convergence set containing the Newton iterates. The rest of the Lipschitz parameters and functions are then defined based on this subset instead of the usual convergence set. This way the resulting parameters and functions are more accurate than in earlier works leading to weaker sufficient semi-local convergence criteria. The novelty of the paper lies in the observation that the new Lipschitz-type functions are special cases of the ones given in earlier works. Therefore, no additional computational effort is required to obtain the new results. The results are applied to solve Hammerstein nonlinear integral equations of Chandrasekhar type in cases not covered by earlier works.