The globalization of Durand-Kerner algorithm (Q1387545)
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scientific article; zbMATH DE number 1159625
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The globalization of Durand-Kerner algorithm |
scientific article; zbMATH DE number 1159625 |
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The globalization of Durand-Kerner algorithm (English)
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9 February 1999
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The construction of a regularly homotopic curve with probability one, based on homotopy theory and the relation between a symmetric polynomial and a polynomial in one variable, is proposed. The discrete tracing along this homotopic curve leads to a class of Durand-Kerner algorithms with stepsizes as parameters. The convergence of this class of algorithms is known, which solves the conjecture about the global property of the Durand-Kerner algorithm. The problem for steplength selection is also discussed. For the verification of the proposed theory a numerical example is given.
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continuous homotopy
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path tracing
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global convergence
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point estimation
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Durand-Kerner algorithms
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steplength selection
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