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In this paper, we give a new bound for the largest singular value of nonnegative rectangular tensors when m = n, which is tighter than the bound provided by Yang and Yang in “Singular values of nonnegative rectangular tensors”, Front. Math. China, 2011, 6, 363-378.

Boundary value problems and controllability of linear systems with right invertible operators [Book]

Nguyen Van Mau (1992)

Bounds and inequalities for the Perron root of a nonnegative matrix. III: Bounds dependent on simple paths and circuits.

Kolotilina, L.Yu. (2005)

Zapiski Nauchnykh Seminarov POMI

Bounds for Exponents of Doubly Stochastic Primitive Matrices.

Mordechai Lewin (1974)

Mathematische Zeitschrift

Bounds for graph expansions via elasticity.

Neumann, Michael, Ormes, Nic (2003)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Bounds for index of a modified graph

Bo Zhou (2004)

Discussiones Mathematicae Graph Theory

If a graph is connected then the largest eigenvalue (i.e., index) generally changes (decreases or increases) if some local modifications are performed. In this paper two types of modifications are considered: (i) for a fixed vertex, t edges incident with it are deleted, while s new edges incident with it are inserted; (ii) for two non-adjacent vertices, t edges incident with one vertex are deleted, while s new edges incident with the other vertex are inserted. ...

Bounds for sine and cosine via eigenvalue estimation

Pentti Haukkanen, Mika Mattila, Jorma K. Merikoski, Alexander Kovacec (2014)

Special Matrices

Define n × n tridiagonal matrices T and S as follows: All entries of the main diagonal of T are zero and those of the first super- and subdiagonal are one. The entries of the main diagonal of S are two except the (n, n) entry one, and those of the first super- and subdiagonal are minus one. Then, denoting by λ(·) the largest eigenvalue, [...] Using certain lower bounds for the largest eigenvalue, we provide lower bounds for these expressions and, further, lower bounds for sin x and cos x on certain...

Bounds for the inverses of diagonally dominant pentadiagonal matrices.

Huang, Zhuohong, Liu, Jianzhou (2010)

Applied Mathematics E-Notes [electronic only]

Bounds for the (Laplacian) spectral radius of graphs with parameter $α$

Gui-Xian Tian, Ting-Zhu Huang (2012)

Czechoslovak Mathematical Journal

Let $G$ be a simple connected graph of order $n$ with degree sequence $(d_{1}, d_{2}, ..., d_{n})$ . Denote ${(^{α} t)}_{i} = \sum_{j : i \sim j} d_{j}^{α}$ , ${(^{α} m)}_{i} = {(^{α} t)}_{i} / d_{i}^{α}$ and ${(^{α} N)}_{i} = \sum_{j : i \sim j} {(^{α} t)}_{j}$ , where $α$ is a real number. Denote by $λ_{1} (G)$ and $μ_{1} (G)$ the spectral radius of the adjacency matrix and the Laplacian matrix of $G$ , respectively. In this paper, we present some upper and lower bounds of $λ_{1} (G)$ and $μ_{1} (G)$ in terms of ${(^{α} t)}_{i}$ , ${(^{α} m)}_{i}$ and ${(^{α} N)}_{i}$ . Furthermore, we also characterize some extreme graphs which attain these upper bounds. These results theoretically improve and generalize some known results.

Bounds for the minimum eigenvalue of a symmetric Toeplitz matrix.

Voss, Heinrich (1999)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Bounds for the singular values of a matrix involving its sparsity pattern.

Kolotilina, L.Yu. (2005)

Zapiski Nauchnykh Seminarov POMI

Bounds for the spectral radius of block $H$ -matrices.

Zhang, Wei, Han, Zheng-Zhi (2006)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Bounds for the spectral radius of nonnegative matrices

Bo Zhou (2001)

Mathematica Slovaca

Bounds for the Z-eigenpair of general nonnegative tensors

Qilong Liu, Yaotang Li (2016)

Open Mathematics

In this paper, we consider the Z-eigenpair of a tensor. A lower bound and an upper bound for the Z-spectral radius of a weakly symmetric nonnegative irreducible tensor are presented. Furthermore, upper bounds of Z-spectral radius of nonnegative tensors and general tensors are given. The proposed bounds improve some existing ones. Numerical examples are reported to show the effectiveness of the proposed bounds.

Bounds for Vandermonde type determinants of orthogonal polynomials.

Schmeisser, Gerhard (2002)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

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