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

Convergence conditions for Secant-type methods

Ioannis K. Argyros, Said Hilout (2010)

Czechoslovak Mathematical Journal

Similarity:

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...