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Expanding the applicability of the Secant method under weaker conditions

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

Abstract

We present a new semilocal convergence analysis for Secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost on the parameters involved our convergence criteria are weaker and the error bounds more precise than in earlier studies such as (Amat and Busquier, 2003; Amat et al., in press; Argyros and Hilout, 2012; Argyros et al., 2014; Argyros and Magreñán, 2014, 2015; Dennis, 1971; Ezquerro et al., 2000; Ortega and Rheinboldt, 1970; Potra and Pták, 1984; Schmidt, 1978). Numerical examples are also presented to illustrate the theoretical results obtained in this study.

Suggested Citation

  • Argyros, Ioannis K. & Magreñán, Á. Alberto, 2015. "Expanding the applicability of the Secant method under weaker conditions," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1000-1012.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:1000-1012
    DOI: 10.1016/j.amc.2015.06.037
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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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