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pro vyhledávání: '"Neiger, A."'
Given polynomials $g$ and $f_1,\dots,f_p$, all in $\Bbbk[x_1,\dots,x_n]$ for some field $\Bbbk$, we consider the problem of computing the critical points of the restriction of $g$ to the variety defined by $f_1=\cdots=f_p=0$. These are defined by the
Externí odkaz:
http://arxiv.org/abs/2402.07353
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 $A^k u_j$ admits a particular basis -- the \emph{maximal Krylov basis} -- which consists of
Externí odkaz:
http://arxiv.org/abs/2402.07345
Autor:
Neiger, Vincent1 vincent.neiger@lip6.fr, Salvy, Bruno2 bruno.salvy@inria.fr, Schost, Éric3 eschost@uwaterloo.ca, Villard, Gilles4 gilles.villard@cnrs.fr
Publikováno v:
Journal of the ACM. Apr2024, Vol. 71 Issue 2, p1-79. 79p.
Autor:
Beelen, Peter, Neiger, Vincent
In this article, we present a fast algorithm performing an instance of the Guruswami-Sudan list decoder for algebraic geometry codes. We show that any such code can be decoded in $\tilde{O}(s^2\ell^{\omega-1}\mu^{\omega-1}(n+g) + \ell^\omega \mu^\ome
Externí odkaz:
http://arxiv.org/abs/2304.07083
We consider the problem of computing a grevlex Gr\"obner basis for the set $F_r(M)$ of minors of size $r$ of an $n\times n$ matrix $M$ of generic linear forms over a field of characteristic zero or large enough. Such sets are not regular sequences; i
Externí odkaz:
http://arxiv.org/abs/2302.05375
The $N$th power of a polynomial matrix of fixed size and degree can be computed by binary powering as fast as multiplying two polynomials of linear degree in~$N$. When Fast Fourier Transform (FFT) is available, the resulting complexity is \emph{softl
Externí odkaz:
http://arxiv.org/abs/2302.04299
Consider a matrix $\mathbf{F} \in \mathbb{K}[x]^{m \times n}$ of univariate polynomials over a field $\mathbb{K}$. We study the problem of computing the column rank profile of $\mathbf{F}$. To this end we first give an algorithm which improves the mi
Externí odkaz:
http://arxiv.org/abs/2202.09329
Solving zero-dimensional polynomial systems using Gr\"obner bases is usually done by, first, computing a Gr\"obner basis for the degree reverse lexicographic order, and next computing the lexicographic Gr\"obner basis with a change of order algorithm
Externí odkaz:
http://arxiv.org/abs/2202.09226
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 polynomials are bounded by $n$, the algorithm uses $O(n^{1.43})$ field operations, breaking through t
Externí odkaz:
http://arxiv.org/abs/2110.08354
Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences whose elements are vecto
Externí odkaz:
http://arxiv.org/abs/2102.03583