Ball convergence for an eighth order efficient method under weak conditions in Banach spaces

Ioannis K. Argyros, Santhosh George, Shobha M. Erappa

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We present a local convergence analysis of an eighth order- iterative method in order to approximate a locally unique solution of an equation in Banach space setting. Earlier studies have used hypotheses up to the fourth derivative although only the first derivative appears in the definition of these methods. In this study we only use the hypothesis on the first derivative. This way we expand the applicability of these methods. Moreover, we provide a radius of convergence, a uniqueness ball and computable error bounds based on Lipschitz constants. Numerical examples computing the radii of the convergence balls as well as examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.

Original languageEnglish
Pages (from-to)513-521
Number of pages9
JournalSeMA Journal
Volume74
Issue number4
DOIs
Publication statusPublished - 12-2017

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Modelling and Simulation
  • Numerical Analysis
  • Control and Optimization

Fingerprint

Dive into the research topics of 'Ball convergence for an eighth order efficient method under weak conditions in Banach spaces'. Together they form a unique fingerprint.

Cite this