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Convergence Analysis and Complex Geometry of an Efficient Derivative-Free Iterative Method

Author

Listed:
  • Deepak Kumar

    (Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, Sangrur, India
    Chandigarh University, Gharuan 140413, Mohali, India
    These authors contributed equally to this work.)

  • Janak Raj Sharma

    (Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, Sangrur, India
    These authors contributed equally to this work.)

  • Lorentz Jäntschi

    (Department of Physics and Chemistry, Technical University of Cluj-Napoca, Cluj-Napoca 400114, Romania
    Institute of Doctoral Studies, Babeş-Bolyai University, Cluj-Napoca 400084, Romania)

Abstract

To locate a locally-unique solution of a nonlinear equation, the local convergence analysis of a derivative-free fifth order method is studied in Banach space. This approach provides radius of convergence and error bounds under the hypotheses based on the first Fréchet-derivative only. Such estimates are not introduced in the earlier procedures employing Taylor’s expansion of higher derivatives that may not exist or may be expensive to compute. The convergence domain of the method is also shown by a visual approach, namely basins of attraction. Theoretical results are endorsed via numerical experiments that show the cases where earlier results cannot be applicable.

Suggested Citation

  • Deepak Kumar & Janak Raj Sharma & Lorentz Jäntschi, 2019. "Convergence Analysis and Complex Geometry of an Efficient Derivative-Free Iterative Method," Mathematics, MDPI, vol. 7(10), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:919-:d:273090
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