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Newton–Kantorovich Convergence Theorem of a Modified Newton’s Method Under the Gamma-Condition in a Banach Space

Author

Listed:
  • M. Chen

    (Zhejiang University)

  • Y. Khan

    (Zhejiang University)

  • Q. Wu

    (Zhejiang University)

  • A. Yildirim

    (University of South Florida
    Ege University)

Abstract

A Newton–Kantorovich convergence theorem of a modified Newton’s method having third order convergence is established under the gamma-condition in a Banach space to solve nonlinear equations. It is assumed that the nonlinear operator is twice Fréchet differentiable and satisfies the gamma-condition. We also present the error estimate to demonstrate the efficiency of our approach. A comparison of our numerical results with those obtained by other Newton–Kantorovich convergence theorems shows high accuracy of our results.

Suggested Citation

  • M. Chen & Y. Khan & Q. Wu & A. Yildirim, 2013. "Newton–Kantorovich Convergence Theorem of a Modified Newton’s Method Under the Gamma-Condition in a Banach Space," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 651-662, June.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:3:d:10.1007_s10957-012-0237-9
    DOI: 10.1007/s10957-012-0237-9
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    Cited by:

    1. Daya Ram Sahu & Jen Chih Yao & Vipin Kumar Singh & Satyendra Kumar, 2017. "Semilocal Convergence Analysis of S-iteration Process of Newton–Kantorovich Like in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 102-127, January.

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