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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.16 No.4

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CONVERGENCE THEOREMS FOR NEWTON'S AND MODIFIED NEWTON'S METHODS

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
2009, v.16 no.4, pp.405-416
Argyros, Ioannis K.
Argyros,, I. K. (2009). CONVERGENCE THEOREMS FOR NEWTON'S AND MODIFIED NEWTON'S METHODS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 16(4), 405-416.

Abstract

In this study we are concerned with the problem of approximating a locally unique solution of an equation in a Banach space setting using Newton's and modified Newton's methods. We provide weaker convergence conditions for both methods than before [5]-[7]. Then, we combine Newton's with the modified Newton's method to approximate locally unique solutions of operator equations. Finer error estimates, a larger convergence domain, and a more precise information on the location of the solution are obtained under the same or weaker hypotheses than before [5]-[7]. The results obtained here improve our earlier ones reported in [4]. Numerical examples are also provided.

keywords
Banach space, Newton-Kantorovich method, radius of convergence, <tex> $Fr{\acute{e}}chet$</tex>-derivative, Banach Lemma on invertible operators

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

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