Advances in the Semilocal Convergence of Newton’s Method with Real-World Applications

Ioannis K. Argyros, Á. Alberto Magreñán, Lara Orcos and Íñigo Sarría
Additional contact information
Ioannis K. Argyros: Department of Mathematics Sciences Lawton, Cameron University, Lawton, OK 73505, USA
Á. Alberto Magreñán: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006 Logroño, Spain
Lara Orcos: Departamento de Matemática Aplicada, Universidad Politècnica de València, 46022 València, Spain
Íñigo Sarría: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño; Spain

Mathematics, 2019, vol. 7, issue 3, 1-12

Abstract: The aim of this paper is to present a new semi-local convergence analysis for Newton’s method in a Banach space setting. The novelty of this paper is that by using more precise Lipschitz constants than in earlier studies and our new idea of restricted convergence domains, we extend the applicability of Newton’s method as follows: The convergence domain is extended; the error estimates are tighter and the information on the location of the solution is at least as precise as before. These advantages are obtained using the same information as before, since new Lipschitz constant are tighter and special cases of the ones used before. Numerical examples and applications are used to test favorable the theoretical results to earlier ones.

Keywords: Banach space; Newton’s method; semi-local convergence; Kantorovich hypothesis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/3/299/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/3/299/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:3:p:299-:d:216781

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().