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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.13 No.4

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Local Convergence of Newton's Method for Perturbed Generalized Equations

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2006, v.13 no.4, pp.261-267
Argyros Ioannis K.
Argyros, I. K. (2006). Local Convergence of Newton's Method for Perturbed Generalized Equations. , 13(4), 261-267.

Abstract

A local convergence analysis of Newton's method for perturbed generalized equations is provided in a Banach space setting. Using center Lipschitzian conditions which are actually needed instead of Lipschitzian hypotheses on the <TEX>$Fr\'{e}chet$</TEX>-derivative of the operator involved and more precise estimates under less computational cost we provide a finer convergence analysis of Newton's method than before [5]-[7].

keywords
Newton's method, Banach space, generalized equation with perturbation, <tex> $Fr\'{e}chet$</tex> derivative, center-Lipschitz, Lipschitz condition, local convergence, variational inequalities

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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