Displaying similar documents to “A Hölderian FCLT for some multiparameter summation process of independent non-identically distributed random variables.”

New sufficient convergence conditions for the secant method

Ioannis K. Argyros (2005)

Czechoslovak Mathematical Journal

Similarity:

We provide new sufficient 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 “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 the earlier ones and under our convergence hypotheses we can cover cases where the earlier conditions are violated. ...