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On the Semilocal Convergence of the Multi–Point Variant of Jarratt Method: Unbounded Third Derivative Case

Author

Listed:
  • Zhang Yong

    (School of Mathematics and Physics, Changzhou University, Changzhou 213164, China)

  • Neha Gupta

    (Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462003, India)

  • J. P. Jaiswal

    (Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462003, India)

  • Kalyanasundaram Madhu

    (Department of Mathematics, Saveetha Engineering College, Chennai 602105, India)

Abstract

In this paper, we study the semilocal convergence of the multi-point variant of Jarratt method under two different mild situations. The first one is the assumption that just a second-order Fréchet derivative is bounded instead of third-order. In addition, in the next one, the bound of the norm of the third order Fréchet derivative is assumed at initial iterate rather than supposing it on the domain of the nonlinear operator and it also satisfies the local ω -continuity condition in order to prove the convergence, existence-uniqueness followed by a priori error bound. During the study, it is noted that some norms and functions have to recalculate and its significance can be also seen in the numerical section.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:540-:d:239605
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    References listed on IDEAS

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    1. 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.
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