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Bounds on the Spectral Norm and the Nuclear Norm of a Tensor Based on Tensor Partitions [PDF]

SIAM Journal on Matrix Analysis and Applications, 2016
Summary: It is known that computing the spectral norm and the nuclear norm of a tensor is NP-hard in general. In this paper, we provide neat bounds for the spectral norm and the nuclear norm of a tensor based on tensor partitions. The spectral norm (respectively, the nuclear norm) can be lower and upper bounded by manipulating the spectral norms ...
Zhening Li
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Spectral norm of random matrices

Proceedings of the thirty-seventh annual ACM symposium on Theory of computing, 2005
This paper studies symmetric random matrices with independent (but not necessarily identical) random variables. It improves an earlier result of \textit{Z.~Füredi} and \textit{J.~Komlós} [Combinatorica 1, 233-241 (1981; Zbl 0494.15010)] on the spectral norm of it. The proof uses Wigner's trace method and a new coding scheme.
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Spectral Norm of Circulant-Type Matrices

Journal of Theoretical Probability, 2009
The convergence in probability and in distribution of the spectral norm of scaled Toeplitz, circulant, reverse circulant, symmetric circulant and a class of \(k\)-circulant matrices is studied as the size of the matrices grows, when the input sequence is independent and identically distributed with finite moments of suitable order. Given its first row,
Bose, Arup, Hazra, Rajat Subhra, Saha, Koushik   +2 more
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On the spectral abscissa and the logarithmic norm

Mathematical Notes, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A I Perov, I D Kostrub, Perov A I
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On the Norm and Spectral Radius

Linear and Multilinear Algebra, 1974
(1974). On the Norm and Spectral Radius. Linear and Multilinear Algebra: Vol. 2, No. 3, pp. 239-240.
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Spectral norms on valued fields

Mathematische Zeitschrift, 2001
Let \((K,|.|)\) be a perfect valued field, \(\bar{K}\) an algebraic closure of \(K\) and \(|.|\) the extension to \(\bar{K}\). Let \(G\) be the group of all \(K\)-automorphisms of \(\bar{K}\) and \(||x||:= \sup \{|\sigma x|\mid \sigma \in G\}\), the \(G\)-spectral norm on \(\bar K\).
Pasol, Vicentiu, Popescu, Angel, Popescu, Nicolae   +2 more
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On the spectral norm of algebraic numbers

Mathematische Nachrichten, 2003
AbstractIn this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure \documentclass{article} \usepackage{amssymb} \pagestyle{empty} \begin{document} $ \overline {\mathbb Q} $ \end{document} of ℚ in ℂ.
Popescu, Angel, Popescu, Nicolae, Zaharescu, Alexandru   +2 more
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On thep-norm joint spectral radius

Journal of Zhejiang University SCIENCE, 2003
The p-norm joint spectral radius is defined by a bounded collection of square matrices with complex entries and of the same size. In the present paper the author investigates the p-norm joint spectral radius for integers. The method introduced in this paper yields some basic formulas for these spectral radii.
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Spectral norm of oriented graphs

Linear Algebra and its Applications, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Carlos Hoppen, Juan Monsalve, Vilmar Trevisan   +2 more
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Spectral norm and nuclear norm of a third order tensor

Journal of Industrial and Management Optimization, 2021
Liqun Qi, Shenglong Hu
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