On constructing two-point optimal fourth-order multiple-root finders with a generic error corrector and illustrating their dynamics (Q1723310)
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scientific article; zbMATH DE number 7025335
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On constructing two-point optimal fourth-order multiple-root finders with a generic error corrector and illustrating their dynamics |
scientific article; zbMATH DE number 7025335 |
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On constructing two-point optimal fourth-order multiple-root finders with a generic error corrector and illustrating their dynamics (English)
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19 February 2019
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Summary: With an error corrector via principal branch of the \(m\)th root of a function-to-function ratio, we propose optimal quartic-order multiple-root finders for nonlinear equations. The relevant optimal order satisfies Kung-Traub conjecture made in 1974. Numerical experiments performed for various test equations demonstrate convergence behavior agreeing with theory and the basins of attractions for several examples are presented.
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