On the convergence of Schröder iteration functions for pth roots of complex numbers (Q546063)
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scientific article; zbMATH DE number 5912688
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the convergence of Schröder iteration functions for pth roots of complex numbers |
scientific article; zbMATH DE number 5912688 |
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On the convergence of Schröder iteration functions for pth roots of complex numbers (English)
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24 June 2011
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Based on the properties the coefficients of the Taylor series of a certain function, a condition on the starting points that guarantees the convergence of the Schröder iteration functions of any order to a \(p\)-th root of a complex number is given. What is of interest is that the iteration functions for \(p\)-th roots of complex scalars can be extended to the matrix case.
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basins of attraction
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Schröder iteration function
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order of convergence
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\(p\)-th root
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residuals
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Taylor expansions
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complex number
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