Some new variants of Newton's method. (Q1764581)
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scientific article; zbMATH DE number 2138641
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some new variants of Newton's method. |
scientific article; zbMATH DE number 2138641 |
Statements
Some new variants of Newton's method. (English)
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25 February 2005
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The paper is devoted to the study of some hybrid Newton-type methods of the form \[ x_{n+1}=x_n-\frac{f(x_n)}{E(f,x_n)}, \] where \(E(f,x_n)\) is either \(\frac{2f'(x_n)f'(z_{n+1})}{f'(x_n)+f'(z_{n+1})}\) or \(f'((x_n+x_{n+1})/2)\), with \[ z_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}. \]
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Newton's method
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harmonic mean Newton's method
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midpoint Newton's method
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convergence
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0.9155772
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0.89300513
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0.8867921
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