Výsledky vyhledávání - "Guérin, Frederic"

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On the Geometry of the Birkhoff Polytope. II. The Schatten $p$-norms

Autor: Bouthat, Ludovick, Mashreghi, Javad, Morneau-Guérin, Frédéric

In the first of this series of two articles, we studied some geometrical aspects of the Birkhoff polytope, the compact convex set of all $n \times n$ doubly stochastic matrices, namely the Chebyshev center, and the Chebyshev radius of the Birkhoff po

Externí odkaz: http://arxiv.org/abs/2310.14043

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On the Geometry of the Birkhoff Polytope. I. The operator $\ell^p_n$-norms

Autor: Bouthat, Ludovick, Mashreghi, Javad, Morneau-Guérin, Frédéric

The geometry of the Birkhoff polytope, i.e., the compact convex set of all $n \times n$ doubly stochastic matrices, has been an active subject of research. While its faces, edges and facets as well as its volume have been intensely studied, other geo

Externí odkaz: http://arxiv.org/abs/2310.14041

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Weighted averages of $\ell^p$ sequences

Autor: Bouthat, Ludovick, Mashreghi, Javad, Morneau-Guérin, Frédéric

The objective of the present paper is to establish three Hardy-type inequalities in which the arithmetic mean over a sequence of non-negative real numbers is replaced by some weighted arithmetic mean over some nested subsets of the given sequence of

Externí odkaz: http://arxiv.org/abs/2306.05586

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On a question of Erd\H{o}s on doubly stochastic matrices

Autor: Bouthat, Ludovick, Mashreghi, Javad, Morneau-Guérin, Frédéric

In a celebrated paper of Marcus and Ree (1959), it was shown that if $A=[a_{ij}]$ is an $n \times n$ doubly stochastic matrix, then there is a permutation $\sigma \in S_n$ such that $\sum_{i,j=1}^{n} a_{i,j}^{2} \leq \sum_{i=1}^{n} a_{i,\sigma(i)}$.

Externí odkaz: http://arxiv.org/abs/2306.05518

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The $p$-norm of circulant matrices

Autor: Bouthat, Ludovick, Khare, Apoorva, Mashreghi, Javad, Morneau-Guérin, Frédéric

Publikováno v: Linear and Multilinear Algebra 70 (2022), no. 21, 7176-7188

In this note we study the induced $p$-norm of circulant matrices $A(n,\pm a, b)$, acting as operators on the Euclidean space $\mathbb{R}^n$. For circulant matrices whose entries are nonnegative real numbers, in particular for $A(n,a,b)$, we provide a

Externí odkaz: http://arxiv.org/abs/2109.09728

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