• Publications
  • Influence
On the complexity of polynomial matrix computations
TLDR
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
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Lattice-based memory allocation
TLDR
We investigate the problem of memory reuse in order to reduce the memory needed to store an array variable. Expand
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On computing the determinant and Smith form of an integer matrix
TLDR
A probabilistic algorithm is presented to find the determinant of a nonsingular, integer matrix. Expand
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Community-Acquired Pneumonia: A Prospective Outpatient Study
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 outpatientExpand
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Further analysis of Coppersmith's block Wiedemann algorithm for the solution of sparse linear systems (extended abstract)
  • G. Villard
  • Mathematics, Computer Science
  • ISSAC
  • 1 July 1997
TLDR
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
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LINBOX: A GENERIC LIBRARY FOR EXACT LINEAR ALGEBRA
TLDR
We describe the design of this generic library, sketch its current range of capabilities, and give several examples of its use. Expand
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On the complexity of computing determinants
TLDR
We present new baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems. Expand
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Normal forms for general polynomial matrices
TLDR
We present an algorithm for the computation of a shifted Popov normal form of a rectangular polynomial matrix. Expand
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An LLL-reduction algorithm with quasi-linear time complexity: extended abstract
TLDR
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
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Efficient matrix preconditioners for black box linear algebra
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 obtainExpand
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