On a Quadratically Convergent Iterative Method Using Divided Differencesof Order One

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2007, v.14 no.3, pp.203-221

Argyros, Ioannis K. (DEPARTMENT OF MATHEMATICAL SCIENCES, CAMERON UNIVERSITY)

Argyros, Ioannis K.. (2007). ON A QUADRATICALLY CONVERGENT ITERATIVE METHOD USING DIVIDED DIFFERENCES OF ORDER ONE. 한국수학교육학회지시리즈B:순수및응용수학, 14(3), 203-221.

복사

Abstract

We introduce a new two-point iterative method to approximate solutions of nonlinear operator equations. The method uses only divided differences of order one, and two previous iterates. However in contrast to the Secant method which is of order 1.618..., our method is of order two. A local and a semilocal convergence analysis is provided based on the majorizing principle. Finally the monotone convergence of the method is explored on partially ordered topological spaces. Numerical examples are also provided where our results compare favorably to earlier ones [1], [4], [5], [19].

keywords: Banach space, POTL-space, majorant principle, Secant method, local/semilocal/monotone convergence, radius of convergence, Lipschitz conditions, divided differences

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논문 상세

Vol.14 No.3

ON A QUADRATICALLY CONVERGENT ITERATIVE METHOD USING DIVIDED DIFFERENCES OF ORDER ONE

On a Quadratically Convergent Iterative Method Using Divided Differencesof Order One

Abstract

한국수학교육학회지시리즈B:순수및응용수학