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On a Quadratically Convergent Iterative Method Using Divided Differencesof Order One

Ioannis K. Argyros
한국수학교육학회|2007.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제14권 제3호|pp. 203-221

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주제분류수학

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Abstract

We introduce a new two-point iterative method to approximate solu-tions of nonlinear operator equations. The method uses only divided dierences oforder one, and two previous iterates. However in contrast to the Secant methodwhich is of order 1.618..., our method is of order two. A local and a semilocalconvergence analysis is provided based on the majorizing principle. Finally themonotone convergence of the method is explored on partially ordered topologicalspaces. Numerical examples are also provided where our results compare favorablyto earlier ones [1], [4], [5], [19].

참고문헌 (20)

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  14. "An analog of the process of tangent hyperbolas for general functionalequations" (1953)
  15. "Iterative Solution of Nonlinear Equations in SeveralVariables. Academic Press" (1970)
  16. "A convergence theorem concerning the method of Chord.Revue d'analysenumerique et de theorie de l'approximation" (1992)
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관련 논문AI추천

On an Improved Unified Convergence Analysis for a Certain Class of Euler-Halley Type MethodsIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2006 · 제13권 제3호A QUADRATICALLY CONVERGENT ITERATIVE METHOD FOR NONLINEAR EQUATIONS윤병인, Miodrag S. Petkovic대한수학회 · 대한수학회지2011 · 제48권 제3호The secant method and the generalized divided differences for solving nonlinear operator equationsB. S. Attili장전수학회 · Advanced Studies in Contemporary Mathematics2006 · 제13권 제1호New Sixth-Order Improvements of the Jarratt Method김용일경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제1호SOME MULTI-STEP ITERATIVE SCHEMES FOR SOLVING NONLINEAR EQUATIONS이병수, Arif Rafiq, Ayesha Inam Pasha한국수학교육학회 · 이론수학과 교직수학2013 · 제20권 제4호Local convergence for some third-order iterative methods under weak conditions조열제, Ioannis K. Argyros, Santhosh George대한수학회 · 대한수학회지2016 · 제53권 제4호

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