APPROXIMATING SOLUTIONS OF EQUATIONSBY COMBINING NEWTON-LIKE METHODS

한국수학교육학회지시리즈B:순수및응용수학 / 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.1, pp.35-45

Argyros, Ioannis K. (Department of Mathematical Sciences, Cameron University)

Argyros, Ioannis K.. (2008). APPROXIMATING SOLUTIONS OF EQUATIONS BY COMBINING NEWTON-LIKE METHODS. 한국수학교육학회지시리즈B:순수및응용수학, 15(1), 35-45.

복사

Abstract

In cases sufficient conditions for the semilocal convergence of Newtonlike methods are violated, we start with a modified Newton-like method (whose weaker convergence conditions hold) until we stop at a certain finite step. Then using as a starting guess the point found above we show convergence of the Newtonlike method to a locally unique solution of a nonlinear operator equation in a Banach space setting. A numerical example is also provided.

keywords: Newton-like method, modified Newton-like method, Banach space, semilocal convergence, Frechet-derivative, Newton-Kantorovich-type hypotheses

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Vol.15 No.1

APPROXIMATING SOLUTIONS OF EQUATIONS BY COMBINING NEWTON-LIKE METHODS

APPROXIMATING SOLUTIONS OF EQUATIONSBY COMBINING NEWTON-LIKE METHODS

Abstract

한국수학교육학회지시리즈B:순수및응용수학