ON THE RADIUS OF CONVERGENCE OF SOME NEWTON{TYPE METHODS IN BANACH SPACES

Argyros, Ioannis K.; Argyros, Ioannis K.; Hilout, Said; Hilout, Said

doi:10.7468/jksmeb.2011.18.3.219

P-ISSN1226-0657
E-ISSN2287-6081
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ON THE RADIUS OF CONVERGENCE OF SOME NEWTON{TYPE METHODS IN BANACH SPACES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2011, v.18 no.3, pp.219-230

https://doi.org/10.7468/jksmeb.2011.18.3.219

Argyros, Ioannis K.
Hilout, Said

Argyros,, I. K. , & Hilout,, S. (2011). ON THE RADIUS OF CONVERGENCE OF SOME NEWTON{TYPE METHODS IN BANACH SPACES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 18(3), 219-230, https://doi.org/10.7468/jksmeb.2011.18.3.219

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Abstract

We determine the radius of convergence for some Newton{type methods (NTM) for approximating a locally unique solution of an equation in a Banach space setting. A comparison is given between the radii of (NTM) and Newton's method (NM). Numerical examples further validating the theoretical results are also provided in this study.

keywords: Newton's method, Newton-type method, Banach space, local convergence, radius of convergence, Lipschitz-H<tex> $\ddot{o}$</tex>lder continuity

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Article Contents

Vol.18 No.3

ON THE RADIUS OF CONVERGENCE OF SOME NEWTON{TYPE METHODS IN BANACH SPACES

Abstract

Reference

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics