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IMPROVED CONVERGENCE OF STEFFENSEN’S METHOD FOR APPROXIMATING FIXED POINTS OF OPERATORS IN BANACH SPACE

Ioannis K. Argyros|Hongmin Ren
대한수학회 (The Korean Mathematical Society)|2017.01|대한수학회지 (Journal of the KMS)|제54권 제1호|pp. 17-33

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참고문헌

키워드

fixed pointBanach spacedivided differenceSteffensen's methodlocal-semilocal convergence
주제분류수학

초록

We present a new local as well as a semilocal convergence analysis for Steffensen's method in order to locate fixed points of operators on a Banach space setting. Using more precise majorizing sequences we show under the same or less computational cost that our convergence criteria can be weaker than in earlier studies such as \cite{1,2,3,4,5,6,7,8,9,10,11,12,13}, \cite{21,22}. Numerical examples are provided to illustrate the theoretical results.

Abstract

We present a new local as well as a semilocal convergence analysis for Steffensen's method in order to locate fixed points of operators on a Banach space setting. Using more precise majorizing sequences we show under the same or less computational cost that our convergence criteria can be weaker than in earlier studies such as \cite{1,2,3,4,5,6,7,8,9,10,11,12,13}, \cite{21,22}. Numerical examples are provided to illustrate the theoretical results.

참고문헌 (27)

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  23. A. A. Magrenan, "A new tool to study real dynamics: The convergence plane", Appl. Math. Comput, 248, pp.215~224 (2014)
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