Convergence Conditions for the Secant Method
Argyros, Ioannis K. ; Hilout, Saïd
CUBO, A Mathematical Journal, Tome 12 (2010), / Harvested from Cubo, A Mathematical Journal

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.

Publié le : 2010-03-01
@article{1434,
     title = {Convergence Conditions for the Secant Method},
     journal = {CUBO, A Mathematical Journal},
     volume = {12},
     year = {2010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1434}
}
Argyros, Ioannis K.; Hilout, Saïd. Convergence Conditions for the Secant Method. CUBO, A Mathematical Journal, Tome 12 (2010) . http://gdmltest.u-ga.fr/item/1434/