Chebyshev's approximation algorithms and applications (Q5948720)
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scientific article; zbMATH DE number 1671944
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chebyshev's approximation algorithms and applications |
scientific article; zbMATH DE number 1671944 |
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Chebyshev's approximation algorithms and applications (English)
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12 November 2001
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multipoint iteration
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recurrence relations
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a priori error bounds
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Banach spaces
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numerical tests
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nonlinear integral equations
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0.9325942
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0.9195374
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0.91810155
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0.8990346
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Let \(X,Y\) be Banach spaces, \(F: X \to Y\) a nonlinear twice Fréchet-differentiable operator such that \(F'(x)\) is continuously invertible. To solve the equation \(F(x)=0\) the author derives the family of multipoint iterations, with \(R\)-order three NEWLINE\[NEWLINEy_n=x_n-\Gamma_n F(x_n), \qquad z_n=x_n+\theta (y_n-x_n),NEWLINE\]NEWLINE NEWLINE\[NEWLINEP(x_n,z_n)=\theta^{-1} \Gamma_n [F'(x_n)-F'(z_n)],NEWLINE\]NEWLINE NEWLINE\[NEWLINEx_{n+1}=y_n+1/2 P(x_n,z_n)(y_n-x_n),NEWLINE\]NEWLINE where \(\theta \in (0,1]\), \(\Gamma_n=[F'(x_n)]^{-1}\). The results of numerical tests with nonlinear integral equations are presented.
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