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Cubo (Temuco)

On-line version ISSN 0719-0646

Abstract

ARGYROS, Ioannis K  and  HILOUT, Saïd. Convergence Conditions for the Secant Method. Cubo [online]. 2010, vol.12, n.1, pp.161-174. ISSN 0719-0646.  http://dx.doi.org/10.4067/S0719-06462010000100014.

We provide new sufficient convergence conditions for the convergence of the Secant method to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, Lipschitz-type and center-Lipschitz-type instead of just Lipschitz-type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than earlier ones and under our convergence hypotheses we can cover cases where earlier conditions are violated. Numerical examples are also provided in this study.

Keywords : Secant method; Banach space; majorizing sequence; divided difference; Fréchet-derivative.

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