A fast method for computing the principal \(n\)-th roots of complex matrices (Q1085563)
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scientific article; zbMATH DE number 3982400
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A fast method for computing the principal \(n\)-th roots of complex matrices |
scientific article; zbMATH DE number 3982400 |
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A fast method for computing the principal \(n\)-th roots of complex matrices (English)
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1986
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A quadratically convergent algorithm for the computation of the principal n-th root of complex matrices is developed by starting from a well-known continued fraction method for determining the n-th root of a positive real number. A main tool in the derivation of the first-mentioned algorithm consists in the use of certain properties of block circulant matrices. There is a numerical example for the case \(n=5\). With an error tolerance of 10(-10) the principal 5th root is obtained after 10 iterations.
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principal n-th root of complex matrices
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continued fraction method
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block circulant matrices
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numerical example
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