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

ISSN : 1226-0657

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

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