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Local convergence of an at least sixth-order method in Banach spaces

  • I. K. Argyros
  • S. K. Khattri
  • S. GeorgeEmail author
Article
  • 21 Downloads

Abstract

We present a local convergence analysis of an at least sixth-order family of methods to approximate a locally unique solution of nonlinear equations in a Banach space setting. The semilocal convergence analysis of this method was studied by Amat et al. in (Appl Math Comput 206:164–174, 2008; Appl Numer Math 62:833–841, 2012). This work provides computable convergence ball and computable error bounds. Numerical examples are also provided in this study.

Keywords

Sixth-order methods three-step Newton-like methods Banach space local convergence majorizing sequences recurrent relations recurrent functions 

Mathematics Subject Classification

65H10 65G99 65K10 47H17 49M15 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesCameron UniversityLawtonUSA
  2. 2.Department of EngineeringStord Haugesund University CollegeHaugesundNorway
  3. 3.Department of Mathematical and Computational SciencesNational Institute of Technology KarnatakaMangaluruIndia

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