scholarly journals A new estimate for the spectral radius of nonnegative tensors

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3409-3418 ◽  
Author(s):  
Jingjing Cui ◽  
Guohua Peng ◽  
Quan Lu ◽  
Zhengge Huang
Keyword(s):  
Spectral Radius ◽  
Nonnegative Tensors ◽  
Numerical Example ◽  
Perron Vector

In this paper, we are concerned with the spectral radius of nonnegative tensors. By estimating the ratio of the smallest component and the largest component of a Perron vector, a new bound for the spectral radius of nonnegative tensors is obtained. It is proved that the new bound improves some existing ones. Finally, a numerical example is implemented to show the effectiveness of the proposed bound.

scholarly journals Some inequalities on the spectral radius of nonnegative tensors

2020 ◽  
Vol 18 (1) ◽  
pp. 262-269
Author(s):  
Chao Ma ◽  
Hao Liang ◽  
Qimiao Xie ◽  
Pengcheng Wang
Keyword(s):  
Spectral Radius ◽  
Nonnegative Tensors

Abstract The eigenvalues and the spectral radius of nonnegative tensors have been extensively studied in recent years. In this paper, we investigate the analytic properties of nonnegative tensors and give some inequalities on the spectral radius.

Design of Optimal Fractional Luenberger Observers for Linear Fractional-Order Systems

2017 ◽  
Author(s):  
Arman Dabiri ◽  
Eric A. Butcher
Keyword(s):  
Banach Space ◽  
Spectral Radius ◽  
Fractional Order ◽  
State Transition ◽  
Design Method ◽  
Design Methods ◽  
The State ◽  
Transition Operator ◽  
Fractional Order Systems ◽  
Numerical Example

Optimal fractional Luenberger observers for linear fractional-order systems are developed using the fractional Chebyshev collocation (FCC) method. It is shown that the design method has advantages over existing Luenberger design methods for fractional order systems. To accomplish this, the state transition operator for the solution of linear fractional-order systems is defined in a Banach space and discretized using the FCC method. In addition, the discretized state transition operator is obtained by using the FCC method. Next, the optimal observer gains are obtained by minimizing the spectral radius of the state transition operator for the observer,while ensuring that the observer responds faster than the controller. Finally, a numerical example is provided to demonstrate the validity and the efficiency of the proposed method.

scholarly journals Bounds for spectral radius of nonnegative tensors using matrix-digragh-based approach

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Guimin Liu ◽  
Hongbin Lv
Keyword(s):  
Spectral Radius ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Nonnegative Tensor ◽  
Related Literature ◽  
Numerical Examples ◽  
Nonnegative Tensors

<p style='text-indent:20px;'>We obtain the improved results of the upper and lower bounds for the spectral radius of a nonnegative tensor by its majorization matrix's digraph. Numerical examples are also given to show that our results are significantly superior to the results of related literature.</p>

The spectral radius of maximum weighted cycle

2016 ◽  
Vol 08 (02) ◽  
pp. 1650021
Author(s):  
Lu Lu ◽  
Qiongxiang Huang ◽  
Lin Chen
Keyword(s):  
Spectral Radius ◽  
Weighted Graphs ◽  
Positive Weight ◽  
Vertex Set ◽  
Perron Vector

Let [Formula: see text] denote the set of all weighted cycles with vertex set [Formula: see text], edge set [Formula: see text] and positive weight set [Formula: see text]. A weighted cycle [Formula: see text] is called maximum if [Formula: see text] for any [Formula: see text]. In this paper, we give some properties of the Perron vector for the maximum weighted graphs and then determine the maximum weighted cycle in [Formula: see text].

Some bounds for the spectral radius of nonnegative tensors

2014 ◽  
Vol 130 (2) ◽  
pp. 315-335 ◽  
Author(s):  
Wen Li ◽  
Michael K. Ng
Keyword(s):  
Spectral Radius ◽  
Nonnegative Tensors

scholarly journals Bounds for the Z-spectral radius of nonnegative tensors

SpringerPlus ◽  
2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Jun He ◽  
Yan-Min Liu ◽  
Hua Ke ◽  
Jun-Kang Tian ◽  
Xiang Li
Keyword(s):  
Spectral Radius ◽  
Nonnegative Tensors
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