We re-examine a quadratically convergent method using divided differences of order one in order to approximate a locally unique solution of an equation in a Banach space setting [4, 5, 7]. Recently in [4, 5, 7], using Lipschitz conditions, and a Newton-Kantorovich type approach, we provided a local as well as a semilocal convergence analysis for this method which compares favorably to other methods using two function evaluations such as the Steffensen’s method [1, 3, 13]. Here, we provide an analysis of this method under the gamma condition [6, 7, 19, 20]. In particular, we also show the quadratic convergence of this method. Numerical examples further validating the theoretical results are also provided.
@article{bwmeta1.element.doi-10_2478_s11533-008-0015-y,
author = {Ioannis Argyros and Hongmin Ren},
title = {On a quadratically convergent method using divided differences of order one under the gamma condition},
journal = {Open Mathematics},
volume = {6},
year = {2008},
pages = {262-271},
zbl = {1152.65063},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0015-y}
}
Ioannis Argyros; Hongmin Ren. On a quadratically convergent method using divided differences of order one under the gamma condition. Open Mathematics, Tome 6 (2008) pp. 262-271. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0015-y/
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