On controlling the residuals of some iterative methods (Q2782922)
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scientific article; zbMATH DE number 1725730
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On controlling the residuals of some iterative methods |
scientific article; zbMATH DE number 1725730 |
Statements
8 April 2002
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nonlinear operator equations
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Banach space
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residuals
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Steffensen-Aitken method
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convergence
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error analysis
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On controlling the residuals of some iterative methods (English)
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The paper deals with inexact Steffensen-Aitken type methods to approximate a locally unique solution of the equation \(F(x)+G(x)=0\), where \(F, G\) are continuous operators defined on a convex subset of a Banach space \(E\) with values in \(E\). The author provides a semilocal convergence theorem as well as an error analysis for proposed the Steffensen-Aitken-like method. A criterion for controlling the residuals to ensure convergence of this method to the solution is also given.
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