Regions of convergence of a Padé family of iterations for the matrix sector function and the matrix \(p\)th root (Q442727)
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scientific article; zbMATH DE number 6063173
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regions of convergence of a Padé family of iterations for the matrix sector function and the matrix \(p\)th root |
scientific article; zbMATH DE number 6063173 |
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Regions of convergence of a Padé family of iterations for the matrix sector function and the matrix \(p\)th root (English)
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3 August 2012
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The authors prove a conjecture on a common region of convergence of Padé iterations for the matrix sector function. Their proof hinges on a useful identity for the hypergeometric function and an explicit expression for the error of the Padé approximation. The results of the paper are illustrated by numerical experiments.
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matrix sector function
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matrix root
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rational matrix iteration
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Padé approximant
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hypergeometric function
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hypergeometric identity
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region of convergence
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numerical experiments
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