Local convergence of a novel eighth order method under hypotheses only on the first derivative

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

Research output: Contribution to journalArticle

Abstract

We expand the applicability of eighth order-iterative method stud- ied by Jaiswal in order to approximate a locally unique solution of an equation in Banach space setting. We provide a local convergence analysis using only hypotheses on the first Frechet-derivative. Moreover, we provide computable convergence radii, error bounds, and uniqueness results. 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)96-107
Number of pages12
JournalKhayyam Journal of Mathematics
Volume5
Issue number2
DOIs
Publication statusPublished - 01-01-2019
Externally publishedYes

Fingerprint

Local Convergence
Derivative
Convergence Ball
Radius
Fréchet Derivative
Convergence Analysis
Unique Solution
Error Bounds
Expand
Uniqueness
Banach space
Iteration
Numerical Examples
Computing

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Argyros, Ioannis K. ; George, Santhosh ; Erappa, Shobha M. / Local convergence of a novel eighth order method under hypotheses only on the first derivative. In: Khayyam Journal of Mathematics. 2019 ; Vol. 5, No. 2. pp. 96-107.
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Local convergence of a novel eighth order method under hypotheses only on the first derivative. / Argyros, Ioannis K.; George, Santhosh; Erappa, Shobha M.

In: Khayyam Journal of Mathematics, Vol. 5, No. 2, 01.01.2019, p. 96-107.

Research output: Contribution to journalArticle

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