منابع مشابه
On the rank of certain parametrized elliptic curves
In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.
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Suppose f = p/q is a quotient of two polynomials and that p has degree rp and q has degree rq . Assume that f(A) and f(A+ uv ) are defined where A ∈ R, u ∈ R, and v ∈ R are given and set r = max{rp, rq}. We show how to compute f(A+uv ) in O(rn2) flops assuming that f(A) is available together with an appropriate factorization of the “denominator matrix” q(A). The central result can be interprete...
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Usage of the Sherman-Morrison-Woodbury formula to update linear systems after low rank modifications of the system matrix is widespread in machine learning. However, it is well known that this formula can lead to serious instabilities in the presence of roundoff error. If the system matrix is symmetric positive definite, it is almost always possible to use a representation based on the Cholesky...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1992
ISSN: 0024-3795
DOI: 10.1016/0024-3795(92)90325-5