We propose algorithms for minimal approximant computation and column reduction that are based on polynomial matrix multiplication; for the determinant, the straight-line program we give also relies on matrix product over <b>K</b>[<i>x</i>.Expand

We initiated a prospective study with a group of practitioners to assess the etiology, clinical presentation, and outcome of community-acquired pneumonia in patients diagnosed in the outpatient… Expand

We analyse the probability of success of the block algorithm proposed by Coppersmith for solving large sparse systems Aw = O of linear equations over a field K. We prove that the input parameters may be tuned such that, for any input system, a solution is computed with high probability for any field.Expand

We devise an algorithm, L1, with the following specifications: It takes as input an arbitrary basis B=(bi)i ∈ Zd x d of a Euclidean lattice L which is reduced for a mild modification of the Lenstra-Lenstra-Lovász reduction; It terminates in time O(d5+ε β) where β = log max |bi| (for any ε>0 and ω is a valid exponent).Expand

Abstract The main idea of the “black box” approach in exact linear algebra is to reduce matrix problems to the computation of minimum polynomials. In most cases preconditioning is necessary to obtain… Expand