Search Results - "Villard, Gilles"

Perturbation Analysis of the QR factor R in the context of LLL lattice basis reduction by Chang, Xiao-Wen, Stehlé, Damien, Villard, Gilles

“…áóá In the present article, we investigate the accuracy of the factor R of the QR factorisation of an LLL-reduced basis. Our main contribution is the first…”
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Bivariate polynomial reduction and elimination ideal over finite fields by Villard, Gilles

“…Given two polynomials a and b in Fq[x,y] which have no non-trivial common divisors, we prove that a generator of the elimination ideal 〈a,b〉∩Fq[x] can be…”
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On the complexity of computing determinants by Kaltofen, Erich, Villard, Gilles

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High precision numerical accuracy in physics research by de Dinechin, Florent, Villard, Gilles

“…Concerns arise that the current standard of double-precision floating-point may no longer be sufficient for today's large-scale numerical simulations. One…”
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Essentially optimal computation of the inverse of generic polynomial matrices by Jeannerod, Claude-Pierre, Villard, Gilles

“…We present an inversion algorithm for nonsingular n× n matrices whose entries are degree d polynomials over a field. The algorithm is deterministic and, when n…”
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High-order lifting for polynomial Sylvester matrices by Pernet, Clément, Signargout, Hippolyte, Villard, Gilles

“…A new algorithm is presented for computing the resultant of two generic bivariate polynomials over an arbitrary field. For p,q in K[x,y] of degree d in x and n…”
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Computing minimal interpolation bases by Jeannerod, Claude-Pierre, Neiger, Vincent, Schost, Éric, Villard, Gilles

“…We consider the problem of computing univariate polynomial matrices over a field that represent minimal solution bases for a general interpolation problem,…”
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Kaltofen’s division-free determinant algorithm differentiated for matrix adjoint computation by Villard, Gilles

“…Kaltofen has proposed a new approach in Kaltofen (1992) for computing matrix determinants without divisions. The algorithm is based on a baby steps/giant steps…”
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Differentiation of Kaltofen's division-free determinant algorithm by Villard, Gilles

“…Kaltofen has proposed a new approach in [Kaltofen 1992] for computing matrix determinants. The algorithm is based on a baby steps/giant steps construction of…”
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Elimination ideal and bivariate resultant over finite fields by Villard, Gilles

“…A new algorithm is presented for computing the largest degree invariant factor of the Sylvester matrix (with respect either to $x$ or $y$) associated to two…”
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Faster Algorithms for Multivariate Interpolation With Multiplicities and Simultaneous Polynomial Approximations by Chowdhury, Muhammad F. I., Jeannerod, Claude-Pierre, Neiger, Vincent, Schost, Eric, Villard, Gilles

“…The interpolation step in the Guruswami-Sudan algorithm is a bivariate interpolation problem with multiplicities commonly solved in the literature using either…”
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Normal forms for general polynomial matrices by Beckermann, Bernhard, Labahn, George, Villard, Gilles

“…We present an algorithm for the computation of a shifted Popov normal form of a rectangular polynomial matrix. For specific input shifts, we obtain methods for…”
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Lattice-based memory allocation by Darte, A., Schreiber, R., Villard, G.

“…We investigate the problem of memory reuse in order to reduce the memory needed to store an array variable. We develop techniques that can lead to smaller…”
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Computing Krylov iterates in the time of matrix multiplication by Neiger, Vincent, Pernet, Clément, Villard, Gilles

“…Krylov methods rely on iterated matrix-vector products $A^k u_j$ for an $n\times n$ matrix $A$ and vectors $u_1,\ldots,u_m$. The space spanned by all iterates…”
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Exact computations with quasiseparable matrices by Pernet, Clément, Signargout, Hippolyte, Villard, Gilles

“…Quasi-separable matrices are a class of rank-structured matriceswidely used in numerical linear algebra and of growing interestin computer algebra, with…”
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Preface by Villard, Gilles

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Computing the sign or the value of the determinant of an integer matrix, a complexity survey by Kaltofen, Erich, Villard, Gilles

“…Computation of the sign of the determinant of a matrix and the determinant itself is a challenge for both numerical and exact methods. We survey the complexity…”
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Faster Modular Composition by Neiger, Vincent, Salvy, Bruno, Schost, Éric, Villard, Gilles

“…A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these…”
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Computing the Characteristic Polynomial of Generic Toeplitz-like and Hankel-like Matrices by Pernet, Clément, Signargout, Hippolyte, Karpman, Pierre, Villard, Gilles

“…New algorithms are presented for computing annihilating polynomials of Toeplitz, Hankel, and more generally Toeplitz+ Hankel-like matrices over a field. Our…”
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Computing an LLL-reduced basis of the orthogonal lattice by Chen, Jingwei, Stehlé, Damien, Villard, Gilles

“…As a typical application, the Lenstra-Lenstra-Lovasz lattice basis reduction algorithm (LLL) is used to compute a reduced basis of the orthogonal lattice for a…”
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