Semilocal convergence theorems for Newton's method using outer inverses and hypotheses on the second Fréchet-derivative (Q5945901)
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scientific article; zbMATH DE number 1657857
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Semilocal convergence theorems for Newton's method using outer inverses and hypotheses on the second Fréchet-derivative |
scientific article; zbMATH DE number 1657857 |
Statements
Semilocal convergence theorems for Newton's method using outer inverses and hypotheses on the second Fréchet-derivative (English)
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14 October 2001
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The author is concerned with Newton's method on a Banach space, where the function \(F(x)\) is a twice Fréchet-differentiable operator defined on an open convex subset \(D\) of the Banach space. The results of the paper can be used to solve undetermined systems, nonlinear least squares problems and ill-posed nonlinear operator problems.
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Newton's method
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Fréchet-derivative
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outer inverse
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generalized inverse
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Banach space
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undetermined systems
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nonlinear least squares problems
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ill-posed nonlinear operator problems
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