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• W2078168416 abstract "A new algorithm is presented for finding the Frobenius rational form F ∈ Zn × nof any A ∈ Zn × nwhich requires an expected number of O(n4(logn + log|| A ||) + n3(logn + log|| A ||)2) word operations using standard integer and matrix arithmetic (where || A || = maxij| Aij|). This substantially improves on the fastest previously known algorithms. The algorithm is probabilistic of the Las Vegas type: it assumes a source of random bits but always produces the correct answer. Las Vegas algorithms are also presented for computing a transformation matrix to the Frobenius form, and for computing the rational Jordan form of an integer matrix." @default.
• W2078168416 created "2016-06-24" @default.
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• W2078168416 date "2002-09-01" @default.
• W2078168416 modified "2023-09-23" @default.
• W2078168416 title "Computing Rational Forms of Integer Matrices" @default.
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• W2078168416 doi "https://doi.org/10.1006/jsco.2002.0554" @default.
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