Weaker convergence conditions for the secant method

Ioannis K. Argyros; Saïd Hilout

Displaying similar documents to “Weaker convergence conditions for the secant method”

On the semilocal convergence of a fast two-step Newton method.

Argyros, Ioannis K. (2008)

Revista Colombiana de Matemáticas

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Convergence conditions for Secant-type methods

Ioannis K. Argyros, Said Hilout (2010)

Czechoslovak Mathematical Journal

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We provide new sufficient convergence conditions for the convergence of the secant-type methods to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, and 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...