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New improved convergence analysis for the secant method

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  • Magreñán, Á. Alberto
  • Argyros, Ioannis K.

Abstract

We present a new convergence analysis, for the secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center–Lipschitz instead of just Lipschitz conditions in the convergence analysis. The new convergence analysis leads to more precise error bounds and to a better information on the location of the solution than the corresponding ones in earlier studies. Numerical examples validating the theoretical results are also provided in this study.

Suggested Citation

  • Magreñán, Á. Alberto & Argyros, Ioannis K., 2016. "New improved convergence analysis for the secant method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 161-170.
    • Handle: RePEc:eee:matcom:v:119:y:2016:i:c:p:161-170
    DOI: 10.1016/j.matcom.2015.08.002
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    Cited by:

    1. Abhimanyu Kumar & D. K. Gupta & Shwetabh Srivastava, 2017. "Influence of the Center Condition on the Two-Step Secant Method," International Journal of Analysis, Hindawi, vol. 2017, pages 1-9, September.

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