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

ISSN : 1226-0657

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Vol.15 No.4

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A COMPARATIVE STUDY BETWEEN CONVERGENCE RESULTS FOR NEWTON'S METHOD

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
2008, v.15 no.4, pp.365-375
Argyros, Ioannis K.
Hilout, Said
Argyros,, I. K. , & Hilout,, S. (2008). A COMPARATIVE STUDY BETWEEN CONVERGENCE RESULTS FOR NEWTON'S METHOD. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 15(4), 365-375.

Abstract

We present a new theorem for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. Under a gamma-type condition we show that we can extend the applicability of Newton's method given in [12]. We also provide a comparative study between results using the classical Newton-Kantorovich conditions ([6], [7], [10]), and the ones using the gamma-type conditions ([12], [13]). Numerical examples are also provided.

keywords
Newton's method, Banach space, Newton-Kantorovich-type hypotheses, gamma-type condition, majorizing sequence, local/semilocal convergence, radius of convergence, Lipschitz conditions

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

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