Local Convergence of Newton's Method for Perturbed Generalized Equations

한국수학교육학회지시리즈B:순수및응용수학 / 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. (DEPARTMENT OF MATHEMATICAL SCIENCES, CAMERON UNIVERSITY)

Argyros Ioannis K.. (2006). LOCAL CONVERGENCE OF NEWTON'S METHOD FOR PERTURBED GENERALIZED EQUATIONS. 한국수학교육학회지시리즈B:순수및응용수학, 13(4), 261-267.

복사

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

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Vol.13 No.4

LOCAL CONVERGENCE OF NEWTON'S METHOD FOR PERTURBED GENERALIZED EQUATIONS

Local Convergence of Newton's Method for Perturbed Generalized Equations

Abstract

한국수학교육학회지시리즈B:순수및응용수학