Displaying similar documents to “Equivalence results for discrete Abel means.”

New sufficient convergence conditions for the secant method

Ioannis K. Argyros (2005)

Czechoslovak Mathematical Journal

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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. ...

Ostrowski-Kantorovich theorem and S -order of convergence of Halley method in Banach spaces

Dong Chen (1993)

Commentationes Mathematicae Universitatis Carolinae

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Ostrowski-Kantorovich theorem of Halley method for solving nonlinear operator equations in Banach spaces is presented. The complete expression of an upper bound for the method is given based on the initial information. Also some properties of S -order of convergence and sufficient asymptotic error bound will be discussed.

Convergence conditions for Secant-type methods

Ioannis K. Argyros, Said Hilout (2010)

Czechoslovak Mathematical Journal

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We provide new sufficient convergence conditions for the convergence of the secant-type methods to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, and 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...