Empirical versus asymptotic rate of convergence of a class of methods for solving a polynomial equation (Q1372037)
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scientific article; zbMATH DE number 1084080
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Empirical versus asymptotic rate of convergence of a class of methods for solving a polynomial equation |
scientific article; zbMATH DE number 1084080 |
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Empirical versus asymptotic rate of convergence of a class of methods for solving a polynomial equation (English)
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4 June 1998
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The authors study alternative methods (with a parameter \(s\)) for solving a polynomial equation. For \(s=0\) this is the Newton-Raphson method, for \(s= 0.5\) they obtain Halley's square-root free method [see \textit{J. F. Traub}, Iterative methods for the solution of equations (1982; Zbl 0472.65040)]. Five examples (including some cases of multiple zeros and clustered zeros) with numerical results are given. Very profound concluding remarks are added.
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asymptotic rate of convergence
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zeros of polynomials
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polynomial equation
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Newton-Raphson method
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Halley's square-root free method
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multiple zeros
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clustered zeros
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0.8727984
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0.86787677
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0.86428046
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0.8640577
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