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of 84
pro vyhledávání: '"Storjohann, Arne"'
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
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:
In Journal of Symbolic Computation May-June 2023 116:146-182
Autor:
Pernet, Clement, Storjohann, Arne
Publikováno v:
Journal of Symbolic Computation, Elsevier, 2018, Special issue on the 41th International Symposium on Symbolic and Alge-braic Computation (ISSAC'16), 85, pp.224-246. \&\#x27E8;10.1016/j.jsc.2017.07.010\&\#x27E9
The class of quasiseparable matrices is defined by the property that any submatrix entirely below or above the main diagonal has small rank, namely below a bound called the order of quasiseparability. These matrices arise naturally in solving PDE's f
Externí odkaz:
http://arxiv.org/abs/1701.00396
Autor:
Nielsen, Johan S. R., Storjohann, Arne
We describe how to solve simultaneous Pad\'e approximations over a power series ring $K[[x]]$ for a field $K$ using $O~(n^{\omega - 1} d)$ operations in $K$, where $d$ is the sought precision and $n$ is the number of power series to approximate. We d
Externí odkaz:
http://arxiv.org/abs/1602.00836
Autor:
Rosenkilde, Johan, Storjohann, Arne
Publikováno v:
In Journal of Symbolic Computation January-February 2021 102:279-303
Transforming a matrix over a field to echelon form, or decomposing the matrix as a product of structured matrices that reveal the rank profile, is a fundamental building block of computational exact linear algebra. This paper surveys the well known v
Externí odkaz:
http://arxiv.org/abs/1112.5717
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Block projections have been used, in [Eberly et al. 2006], to obtain an efficient algorithm to find solutions for sparse systems of linear equations. A bound of softO(n^(2.5)) machine operations is obtained assuming that the input matrix can be multi
Externí odkaz:
http://arxiv.org/abs/cs/0701188
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic complexity in te
Externí odkaz:
http://arxiv.org/abs/cs/0603082