Fast Parallel Algorithms for Matrix Reduction to Normal Forms
نویسندگان
چکیده
منابع مشابه
Parallel Algorithms for Matrix Normal Forms
Here we offer a new randomized parallel algorithm that determines the Smith normal form of a matrix with entries being univariate polynomials with coefficients in an arbitrary field. The algorithm has two important advantages over our previous one: the multipliers relating the Smith form to the input matrix are computed, and the algorithm is probabilistic of Las Vegas type, i.e., always finds t...
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Poursuivant une s erie d'articles sur le calcul de formes normales de matrices, nous nous int eressons ici a la complexit e parall ele du calcul de transformations associ ees. Pour une matrice B de Mn;n(K), o u K est un corps commutatif, nous d emontrons que le probl eme de calculer une matrice de transformation P telle que F = P ?1 BP soit sous forme normale de Frobenius, est dans NC 2 K. Nous...
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A Las Vegas type probabilistic algorithm is presented for nding the Frobenius canonical form of an n n matrix T over any eld K. The algorithm requires O~(MM(n)) = MM(n) (logn) O(1) operations in K, where O(MM(n)) operations in K are suucient to multiply two n n matrices over K. This nearly matches the lower bound of (MM(n)) operations in K for this problem, and improves on the O(n 4) operations...
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ژورنال
عنوان ژورنال: Applicable Algebra in Engineering, Communication and Computing
سال: 1997
ISSN: 0938-1279,1432-0622
DOI: 10.1007/s002000050089