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Displaying similar documents to “Stability and convergence results based on fixed point theory for a generalized viscosity iterative scheme.”

On a quadratically convergent method using divided differences of order one under the gamma condition

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...

A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets

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....