Semilocal convergence conditions for the secant method, using recurrent functions

Ioannis K. Argyros; Saïd Hilout

doi:10.33993/jnaat402-1041

Authors

Ioannis K. Argyros Cameron University, USA
Saïd Hilout Poitiers University, France

DOI:

https://doi.org/10.33993/jnaat402-1041

Keywords:

recurrent functions, semilocal convergence, secant method, Banach space, majorizing sequence, divided difference, Fréchet derivative

Abstract views: 247

Abstract

Using our new concept of recurrent functions, we present new sufficient convergence conditions for the secant method to a locally unique solution of a nonlinear equation in a Banach space. We combine Lipschitz and center-Lipschitz conditions on the divided difference operator to obtain the semilocal convergence analysis of the secant method. Our error bounds are tighter than earlier ones. Moreover, under our convergence hypotheses, we can expand the applicability of the secant method in cases not covered before [8], [9], [12]-[14], [16], [19]-[21]. Application and examples are also provided in this study.

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References

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