On the order of convergence of Broyden-Gay-Schnabel's method
J. M. Martínez (1978)
Commentationes Mathematicae Universitatis Carolinae
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J. M. Martínez (1978)
Commentationes Mathematicae Universitatis Carolinae
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Ansari, A.H., Moslehian, M.S. (2005)
International Journal of Mathematics and Mathematical Sciences
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Ioannis Argyros, Hongmin Ren (2008)
Open Mathematics
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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...
Agarwal, Ravi P., Verma, Ram U. (2009)
Fixed Point Theory and Applications [electronic only]
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Wan, Zhong (2004)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Zabel, Ahmed, Alghamdi, Maryam (2011)
International Journal of Mathematics and Mathematical Sciences
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Gilbert Crombez (2006)
Czechoslovak Mathematical Journal
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The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in a Euclidean space, may lead to slow convergence of the constructed sequence when that sequence enters some narrow “corridor” between two or more convex sets. A way to leave such corridor consists in taking a big step at different moments during the iteration, because in that way the monotoneous behaviour that is responsible for the slow convergence may be interrupted....