A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton–Kantorovich Iterations-II

Samundra Regmi, Ioannis K. Argyros, Santhosh George and Michael I. Argyros
Additional contact information
Samundra Regmi: Department of Mathematics, University of Houston, Houston, TX 77204, USA
Ioannis K. Argyros: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Santhosh George: Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Karnataka 575 025, India
Michael I. Argyros: Department of Computer Science, University of Oklahoma, Norman, OK 73019, USA

Mathematics, 2022, vol. 10, issue 11, 1-12

Abstract: This article is an independently written continuation of an earlier study with the same title [Mathematics, 2022, 10, 1225] on the Newton Process (NP). This process is applied to solve nonlinear equations. The complementing features are: the smallness of the initial approximation is expressed explicitly in turns of the Lipschitz or Hölder constants and the convergence order 1 + p is shown for p ∈ ( 0 , 1 ] . The first feature becomes attainable by further simplifying proofs of convergence criteria. The second feature is possible by choosing a bit larger upper bound on the smallness of the initial approximation. This way, the completed convergence analysis is finer and can replace the classical one by Kantorovich and others. A two-point boundary value problem (TPBVP) is solved to complement this article.

Keywords: iterative processes; Banach space; semi-local convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/11/1839/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/11/1839/ (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:10:y:2022:i:11:p:1839-:d:825424

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 ().