Efficient algorithms for computing the characteristic polynomial in a domain (Q5928850)
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scientific article; zbMATH DE number 1584447
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Efficient algorithms for computing the characteristic polynomial in a domain |
scientific article; zbMATH DE number 1584447 |
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Efficient algorithms for computing the characteristic polynomial in a domain (English)
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3 July 2001
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New sequential methods are given for computing the characteristic polynomial of an endomorphism of a free finite rank-a module over a domain, that require \(O(n^3)\) ring operations with exact division. The Dodgson elimination process is analysed as a sequence of matrices by using Sylvester determinant identity. The Dodgson process is applied for reducing a given square matrix to a similar QT matrix. The algorithm is ilustrated on a numerical example.
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characteristic polynomial
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free finite rank-a module
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Dodgson elimination
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Sylvester determinant identity
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QT matrix
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algorithm
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numerical examples
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