A modification of the Lipschitz condition in the Newton-Kantorovich theorem (Q330251)
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scientific article; zbMATH DE number 6643053
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A modification of the Lipschitz condition in the Newton-Kantorovich theorem |
scientific article; zbMATH DE number 6643053 |
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A modification of the Lipschitz condition in the Newton-Kantorovich theorem (English)
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25 October 2016
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Summary: We analyse the semilocal convergence of Newton's method in Banach spaces under a modification of the classic Lipschitz condition on the first derivative of the operator involved in Kantorovich's theory. For this, we use a technique based on recurrence relations instead of the well-known majorant principle of Kantorovich. We illustrate this analysis with an application where a Hammerstein nonlinear integral equation of the second kind is involved.
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Newton's method
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semilocal convergence
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Newton-Kantorovich theorem
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recurrence relations
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error estimates
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order of convergence
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nonlinear integral equation
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0.9067581295967102
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0.874410092830658
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0.8540208339691162
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