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An algorithm for the exact reduction of a matrix to Frobenius form using modular arithmetic. II

Author: Jo Ann Howell
Journal: Math. Comp. 27 (1973), 905-920
MSC: Primary 65F30
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Abstract: Part I contained a description of the single-modulus algorithm for reducing a matrix to Frobenius form, obtaining exact integral factors of the characteristic polynomial. Part II contains a description of the multiple-modulus algorithm. Since different moduli may yield different factorizations, an algorithm is given for determining which factorizations are not correct factorizations over the integers of the characteristic polynomial. Part II also contains a discussion of the selection of the moduli and numerical examples.

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Keywords: Modular arithmetic, residue arithmetic, modulus, Frobenius form, Danilewski method, characteristic polynomial, similarity transformation, prime number, Chinese Remainder Theorem
Article copyright: © Copyright 1973 American Mathematical Society