An iterative method for finding the spectral radius of an irreducible nonnegative tensor

2021 ◽  
Vol 40 (1) ◽  
Author(s):  
Junli Zhang ◽  
Changjiang Bu
Keyword(s):  
Iterative Method ◽  
Spectral Radius ◽  
Nonnegative Tensor

scholarly journals The Perturbation Bound for the Spectral Radius of a Nonnegative Tensor

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wen Li ◽  
Michael K. Ng
Keyword(s):  
Spectral Radius ◽  
Perturbation Analysis ◽  
Absolute Difference ◽  
Nonnegative Tensor ◽  
Backward Error ◽  
Perturbation Bound ◽  
Error Matrix ◽  
Largest Eigenvalue ◽  
The Stability ◽  
The Largest Eigenvalue

We study the perturbation bound for the spectral radius of an mth-order n-dimensional nonnegative tensor A. The main contribution of this paper is to show that when A is perturbed to a nonnegative tensor A~ by ΔA, the absolute difference between the spectral radii of A and A~ is bounded by the largest magnitude of the ratio of the ith component of ΔAxm-1 and the ith component xm-1, where x is an eigenvector associated with the largest eigenvalue of A in magnitude and its entries are positive. We further derive the bound in terms of the entries of A only when x is not known in advance. Based on the perturbation analysis, we make use of the NQZ algorithm to estimate the spectral radius of a nonnegative tensor in general. On the other hand, we study the backward error matrix ΔA and obtain its smallest error bound for its perturbed largest eigenvalue and associated eigenvector of an irreducible nonnegative tensor. Based on the backward error analysis, we can estimate the stability of computation of the largest eigenvalue of an irreducible nonnegative tensor by the NQZ algorithm. Numerical examples are presented to illustrate the theoretical results of our perturbation analysis.

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>

scholarly journals Some bounds for the Z-eigenpair of nonnegative tensors

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiaoyu Ma ◽  
Yisheng Song
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Radius ◽  
Important Research ◽  
Nonnegative Tensor ◽  
Research Topics ◽  
Nonnegative Tensors ◽  
Tensor Theory ◽  
Weakly Symmetric ◽  
Tensor Eigenvalue

Abstract Tensor eigenvalue problem is one of important research topics in tensor theory. In this manuscript, we consider the properties of Z-eigenpair of irreducible nonnegative tensors. By estimating the ratio of the smallest and largest components of a positive Z-eigenvector for a nonnegative tensor, we present some bounds for the eigenvector and Z-spectral radius of an irreducible and weakly symmetric nonnegative tensor. The proposed bounds complement and extend some existing results. Finally, several examples are given to show that such a bound is different from one given in the literature.

scholarly journals A Method with Parameter for Solving the Spectral Radius of Nonnegative Tensor

2016 ◽  
Vol 5 (1) ◽  
pp. 3-25
Author(s):  
Yi-Yong Li ◽  
Qing-Zhi Yang ◽  
Xi He
Keyword(s):  
Spectral Radius ◽  
Nonnegative Tensor

Quality Improvement of X-ray CT Images by Estimation of the Mechanical Misalignment in a Projection Image Using an Iterative Method

2017 ◽  
Vol 137 (3) ◽  
pp. 213-219
Author(s):  
Kenji Noguchi ◽  
Satoshi Takahashi ◽  
Daisuke Suzuki ◽  
Atsushi Teramoto
Keyword(s):  
Quality Improvement ◽  
Iterative Method ◽  
Ct Images ◽  
X Ray ◽  
Projection Image

THE REALIZATION OF THE ITERATIVE METHOD OF THE LEAST SQUARES FOR THE ESTIMATION OF STATIC OBJECT PARAMETERS IN MATLAB ENVIRONMENT

2017 ◽  
pp. 28-36
Author(s):  
Galina Vasil’evna Troshina ◽  
Alexander Aleksandrovich Voevoda
Keyword(s):  
Parameter Estimation ◽  
Iterative Method ◽  
Least Squares ◽  
Input Signal ◽  
Layer Structure ◽  
Estimation Procedure ◽  
Parameter Estimation Procedure ◽  
Noise Simulation ◽  
Static Object ◽  
Object Parameters

It was suggested to use the system model working in real time for an iterative method of the parameter estimation. It gives the chance to select a suitable input signal, and also to carry out the setup of the object parameters. The object modeling for a case when the system isn't affected by the measurement noises, and also for a case when an object is under the gaussian noise was executed in the MatLab environment. The superposition of two meanders with different periods and single amplitude is used as an input signal. The model represents the three-layer structure in the MatLab environment. On the most upper layer there are units corresponding to the simulation of an input signal, directly the object, the unit of the noise simulation and the unit for the parameter estimation. The second and the third layers correspond to the simulation of the iterative method of the least squares. The diagrams of the input and the output signals in the absence of noise and in the presence of noise are shown. The results of parameter estimation of a static object are given. According to the results of modeling, the algorithm works well even in the presence of significant measurement noise. To verify the correctness of the work of an algorithm the auxiliary computations have been performed and the diagrams of the gain behavior amount which is used in the parameter estimation procedure have been constructed. The entry conditions which are necessary for the work of an iterative method of the least squares are specified. The understanding of this algorithm functioning principles is a basis for its subsequent use for the parameter estimation of the multi-channel dynamic objects.

An adaptive chebyshev iterative method

2018 ◽  
Vol 30 (10) ◽  
pp. 67-85
Author(s):  
V. Zhukov ◽  
◽  
O. Feodoritova ◽  
N. Novikova ◽  
◽  
...  
Keyword(s):  
Iterative Method
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