منابع مشابه
Fast polynomial factorization and modular composition
We obtain randomized algorithms for factoring degree n univariate polynomials over Fq requiring O(n1.5+o(1) log q + n1+o(1) logq) bit operations. When log q < n, this is asymptotically faster than the best previous algorithms [J. von zur Gathen and V. Shoup, Comput. Complexity, 2 (1992), pp. 187–224; E. Kaltofen and V. Shoup, Math. Comp., 67 (1998), pp. 1179– 1197]; for log q ≥ n, it matches th...
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Classes of Abaffy-Broyden-Spedicato (ABS) methods have been introduced for solving linear systems of equations. The algorithms are powerful methods for developing matrix factorizations and many fundamental numerical linear algebra processes. Here, we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW factorizations of a nonsingular matrix as well as...
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Tensor factorization arises in many machinelearning applications, such knowledge basemodeling and parameter estimation in latentvariable models. However, numerical meth-ods for tensor factorization have not reachedthe level of maturity of matrix factorizationmethods. In this paper, we propose a newmethod for CP tensor factorization that usesrandom projections to ...
متن کاملFast polynomial factorization, modular composition, and multipoint evaluation of multivariate polynomials in small characteristic
We obtain randomized algorithms for factoring degree n univariate polynomials over Fq that use O(n + n log q) field operations, when the characteristic is at most n. When log q < n, this is asymptotically faster than the best previous algorithms (von zur Gathen & Shoup (1992) and Kaltofen & Shoup (1998)); for log q ≥ n, it matches the asymptotic running time of the best known algorithms. The im...
متن کاملFactorization in the Composition Algebras
Let O be a maximal arithmetic in one of the four (non-split) composition algebras over R, and let ] = mn be the norm of an element in O. Rehm 15] describes an algorithm for nding all factorizations of as = , where ] = m, ] = n and (m; n) = 1. Here, we extend the algorithm to general , m, and n, providing precise geometrical conngurations for the sets of left-and right-hand divisors.
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2018
ISSN: 0885-064X
DOI: 10.1016/j.jco.2018.05.002