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Second-Derivative-Free Variant of the Chebyshev Method for Nonlinear Equations

Author

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  • M. A. Hernández

    (University of La Rioja)

Abstract

In this paper, we introduce a numerical method for nonlinear equations, based on the Chebyshev third-order method, in which the second-derivative operator is replaced by a finite difference between first derivatives. We prove a semilocal convergence theorem which guarantees local convergence with R-order three under conditions similar to those of the Newton-Kantorovich theorem, assuming the Lipschitz continuity of the second derivative. In a subsequent theorem, the latter condition is replaced by the weaker assumption of Lipschitz continuity of the first derivative.

Suggested Citation

  • M. A. Hernández, 2000. "Second-Derivative-Free Variant of the Chebyshev Method for Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 501-515, March.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:3:d:10.1023_a:1004618223538
    DOI: 10.1023/A:1004618223538
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    Cited by:

    1. Argyros, Ioannis K. & George, Santhosh, 2015. "Ball convergence comparison between three iterative methods in Banach space under hypothese only on the first derivative," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1031-1037.

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