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pro vyhledávání: '"Labahn, A"'
In this paper, we consider the problem of deciding the existence of real solutions to a system of polynomial equations having real coefficients, and which are invariant under the action of the symmetric group. We construct and analyze a Monte Carlo p
Externí odkaz:
http://arxiv.org/abs/2306.03855
A Las Vegas randomized algorithm is given to compute the Hermite normal form of a nonsingular integer matrix $A$ of dimension $n$. The algorithm uses quadratic integer multiplication and cubic matrix multiplication and has running time bounded by $O(
Externí odkaz:
http://arxiv.org/abs/2209.10685
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
A Bohemian matrix family is a set of matrices all of whose entries are drawn from a fixed, usually discrete and hence bounded, subset of a field of characteristic zero. Originally these were integers -- hence the name, from the acronym BOunded HEight
Externí odkaz:
http://arxiv.org/abs/2202.07769
Autor:
Labahn, Jakob, Bittner, Lucas, Hirschmann, Philip, Roettig, Christopher-Bastian, Burghardt, Diana, Glaser, Bruno, Marković, Slobodan B., Zech, Michael
The analysis of the stable oxygen isotopes 18O and 16O has revolutionized paleoclimate research since the middle of the last century. Particularly, δ18O of ice cores from Greenland and Antarctica is used as a paleotemperature proxy, and δ18O of dee
Externí odkaz:
https://tud.qucosa.de/id/qucosa%3A91792
https://tud.qucosa.de/api/qucosa%3A91792/attachment/ATT-0/
https://tud.qucosa.de/api/qucosa%3A91792/attachment/ATT-0/
A Las Vegas randomized algorithm is given to compute the Smith multipliers for a nonsingular integer matrix $A$, that is, unimodular matrices $U$ and $V$ such that $AV=US$, with $S$ the Smith normal form of $A$. The expected running time of the algor
Externí odkaz:
http://arxiv.org/abs/2111.09949
Publikováno v:
MDPI Information 2021, vol. 12 nr. 11, article-nr. 443
Currently, the most widespread neural network architecture for training language models is the so called BERT which led to improvements in various Natural Language Processing (NLP) tasks. In general, the larger the number of parameters in a BERT mode
Externí odkaz:
http://arxiv.org/abs/2104.11559
Let $\mathbf{K}$ be a field and $\phi$, $\mathbf{f} = (f_1, \ldots, f_s)$ in $\mathbf{K}[x_1, \dots, x_n]$ be multivariate polynomials (with $s < n$) invariant under the action of $\mathcal{S}_n$, the group of permutations of $\{1, \dots, n\}$. We co
Externí odkaz:
http://arxiv.org/abs/2009.00847
Let $\mathbf{K}$ be a field of characteristic zero with $\overline{\mathbf{K}}$ its algebraic closure. Given a sequence of polynomials $\mathbf{g} = (g_1, \ldots, g_s) \in \mathbf{K}[x_1, \ldots , x_n]^s$ and a polynomial matrix $\mathbf{F} = [f_{i,j
Externí odkaz:
http://arxiv.org/abs/2009.00844
We present two new algorithms for the computation of the q-integer linear decomposition of a multivariate polynomial. Such a decomposition is essential for the treatment of q-hypergeometric symbolic summation via creative telescoping and for describi
Externí odkaz:
http://arxiv.org/abs/2002.00124