On the geometry of Graeffe iteration (Q5949383)
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scientific article; zbMATH DE number 1675702
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the geometry of Graeffe iteration |
scientific article; zbMATH DE number 1675702 |
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On the geometry of Graeffe iteration (English)
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29 September 2002
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polynomial root
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univariate complex polynomial
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renormalized Graeffe algorithm
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global complexity
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Let \(f\) be a univariate polynomial of degree \(d\). Its Graeffe iterate is defined by NEWLINE\[NEWLINEGf(x)=(-1)^d f(\sqrt{x}) f(-\sqrt{x}).NEWLINE\]NEWLINE NEWLINENEWLINENEWLINEUsing a renormalized variant of Graeffe iteration, the authors design an algorithm which is globally convergent, with probability 1, for finding the absolute values of the roots of univariate complex polynomials.
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