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Semilocal convergence analysis on the modifications for Chebyshev–Halley methods under generalized condition

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  • Wang, Xiuhua
  • Kou, Jisheng

Abstract

In this paper, we consider the semilocal convergence for modifications of Chebyshev–Halley methods in Banach space. Compared with the results on super-Halley method studied in reference Gutiérrez and Hernández (1998)these modified methods need less computation of inversion, the R-order is improved, and the Lipschitz continuity of second derivative is also relaxed. We prove a theorem to show existence-uniqueness of solution. The R-order for these modified methods is analyzed under generalized condition.

Suggested Citation

  • Wang, Xiuhua & Kou, Jisheng, 2016. "Semilocal convergence analysis on the modifications for Chebyshev–Halley methods under generalized condition," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 243-251.
    • Handle: RePEc:eee:apmaco:v:281:y:2016:i:c:p:243-251
    DOI: 10.1016/j.amc.2016.01.035
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    Cited by:

    1. Zhang Yong & Neha Gupta & J. P. Jaiswal & Kalyanasundaram Madhu, 2019. "On the Semilocal Convergence of the Multi–Point Variant of Jarratt Method: Unbounded Third Derivative Case," Mathematics, MDPI, vol. 7(6), pages 1-14, June.

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