On the quadratic convergence of Newton's method under center-Lipschitz but not necessarily Lipschitz hypotheses (Q2843889)
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scientific article; zbMATH DE number 6201659
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the quadratic convergence of Newton's method under center-Lipschitz but not necessarily Lipschitz hypotheses |
scientific article; zbMATH DE number 6201659 |
Statements
26 August 2013
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Newton's method
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Banach space
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majorizing sequences
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Lipschitz condition
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center-Lipschitz condition
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semilocal convergence
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local convergence
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numerical example
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On the quadratic convergence of Newton's method under center-Lipschitz but not necessarily Lipschitz hypotheses (English)
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The paper deals with the convergence of Newton's method in a Banach space. There is a plethora of local as well as semilocal convergence results for Newton's method based on the Lipschitz condition. In 2004, the first author [J. Math. Anal. Appl. 298, No. 2, 374--397 (2004; Zbl 1057.65029)] presented convergence analysis of the method using a combination of Lipschitz condition and the center Lipschitz condition. In this paper, the authors provide new local and semilocal convergence results for Newton's method using only center-Lipschitz condition. Also, they provide a numerical example to show that center-Lipschitz condition holds but not Lipschitz condition.
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