High Order Fixed Point and Newton's Methods in Banach Space. (17th February 2021)

• Record Type: Journal Article
• Authors: Dubeau, François
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 3(2021)
• Page Start: 251
• Page End: 278
• Publication Date: 2021-02-17
• Subjects: Banach space -- fixed point method -- higher order convergence -- necessary conditions -- Newton's method -- sufficient conditions -- Taylor's expansion; 65H10 -- 65J15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1873365
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Through Taylor's expansions and a thorough analysis of the necessary and sufficient conditions that will entail for fixed point and Newton's iterative methods to be of higher order convergence in Banach space, we are able to present a unified way to make these methods faster. Numerical examples illustrate the theoretical results.