scholarly journals Improved Brauer-type eigenvalue localization sets for tensors with their applications

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4607-4625
Author(s):  
Zhengge Huang ◽  
Jingjing Cui
Keyword(s):  
Linear Algebra ◽  
Multilinear Algebra ◽  
Numerical Examples ◽  
Eigenvalue Localization ◽  
New Criteria ◽  
Localization Sets ◽  
Better Than

In this paper, by excluding some sets from the Brauer-type eigenvalue inclusion sets for tensors developed by Bu et al. (Linear Algebra Appl. 512 (2017) 234-248) and Li et al. (Linear and Multilinear Algebra 64 (2016) 727-736), some improved Brauer-type eigenvalue localization sets for tensors are given, which are proved to be much tighter than those put forward by Bu et al. and Li et al. As applications, some new criteria for identifying the nonsingularity of tensors are developed, which are better than some previous results. This fact is illustrated by some numerical examples.

scholarly journals Some improvements on the Ky Fan theorem for tensors

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Mohsen Tourang ◽  
Mostafa Zangiabadi
Keyword(s):  
Multilinear Algebra ◽  
Numerical Examples ◽  
Eigenvalue Localization ◽  
Fan Theorem ◽  
Linear Multilinear Algebra ◽  
Numer Math ◽  
Ky Fan ◽  
Localization Sets ◽  
Ky Fan Theorem ◽  
Perron Vector

AbstractThe improvements of Ky Fan theorem are given for tensors. First, based on Brauer-type eigenvalue inclusion sets, we obtain some new Ky Fan-type theorems for tensors. Second, by characterizing the ratio of the smallest and largest values of a Perron vector, we improve the existing results. Third, some new eigenvalue localization sets for tensors are given and proved to be tighter than those presented by Li and Ng (Numer Math 130(2):315–335, 2015) and Wang et al. (Linear Multilinear Algebra 68(9):1817–1834, 2020). Finally, numerical examples are given to validate the efficiency of our new bounds.

scholarly journals Two new eigenvalue localization sets for tensors and theirs applications

2017 ◽  
Vol 15 (1) ◽  
pp. 1267-1276 ◽  
Author(s):  
Jianxing Zhao ◽  
Caili Sang
Keyword(s):  
Linear Algebra ◽  
Symmetric Tensor ◽  
Sufficient Condition ◽  
Numerical Examples ◽  
Eigenvalue Localization ◽  
Even Order ◽  
Weakly Symmetric ◽  
Localization Set ◽  
Theoretical Results ◽  
Localization Sets

Abstract A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324) and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50). As an application, a weaker checkable sufficient condition for the positive (semi-)definiteness of an even-order real symmetric tensor is obtained. Meanwhile, an S-type E-eigenvalue localization set for tensors is given and proved to be tighter than that presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1), 187-198). As an application, an S-type upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.

scholarly journals New error bounds for linear complementarity problems of Σ-SDD matrices and SB-matrices

2019 ◽  
Vol 17 (1) ◽  
pp. 1599-1614
Author(s):  
Zhiwu Hou ◽  
Xia Jing ◽  
Lei Gao
Keyword(s):  
Linear Algebra ◽  
Error Bound ◽  
Linear Complementarity Problem ◽  
Error Bounds ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Examples ◽  
Numer Algor ◽  
Better Than

Abstract A new error bound for the linear complementarity problem (LCP) of Σ-SDD matrices is given, which depends only on the entries of the involved matrices. Numerical examples are given to show that the new bound is better than that provided by García-Esnaola and Peña [Linear Algebra Appl., 2013, 438, 1339–1446] in some cases. Based on the obtained results, we also give an error bound for the LCP of SB-matrices. It is proved that the new bound is sharper than that provided by Dai et al. [Numer. Algor., 2012, 61, 121–139] under certain assumptions.

scholarly journals A modified S-type eigenvalue localization set of tensors applications

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6395-6416
Author(s):  
Zhengge Huang ◽  
Ligong Wang ◽  
Zhong Xu ◽  
Jingjing Cui
Keyword(s):  
Spectral Radius ◽  
Linear Algebra ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Numerical Examples ◽  
Nonnegative Tensors ◽  
Eigenvalue Localization ◽  
Localization Set ◽  
Weakly Irreducible ◽  
Eigenvalues Of Tensors

Based on the S-type eigenvalue localization set developed by Li et al. (Linear Algebra Appl. 493 (2016) 469-483) for tensors, a modified S-type eigenvalue localization set for tensors is established in this paper by excluding some sets from the existing S-type eigenvalue localization set developed by Huang et al. (arXiv: 1602.07568v1, 2016). The proposed set containing all eigenvalues of tensors is much sharper compared with that employed by Li et al. and Huang et al. As its applications, a criteria, which can be utilized for identifying the nonsingularity of tensors, is developed. In addition, we provide new upper and lower bounds for the spectral radius of nonnegative tensors and the minimum H-eigenvalue of weakly irreducible strong M-tensors. These bounds are superior to some previous results, which is illustrated by some numerical examples.

scholarly journals A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices

2018 ◽  
Vol 16 (1) ◽  
pp. 298-310
Author(s):  
Xiaoxiao Wang ◽  
Chaoqian Li ◽  
Yaotang Li
Keyword(s):  
Linear Algebra ◽  
Complex Plane ◽  
Upper Bound ◽  
Stochastic Matrix ◽  
Multilinear Algebra ◽  
Stochastic Matrices ◽  
Eigenvalue Localization ◽  
Localization Set

AbstractA set in the complex plane which involves n parameters in [0, 1] is given to localize all eigenvalues different from 1 for stochastic matrices. As an application of this set, an upper bound for the moduli of the subdominant eigenvalues of a stochastic matrix is obtained. Lastly, we fix n parameters in [0, 1] to give a new set including all eigenvalues different from 1, which is tighter than those provided by Shen et al. (Linear Algebra Appl. 447 (2014) 74-87) and Li et al. (Linear and Multilinear Algebra 63(11) (2015) 2159-2170) for estimating the moduli of subdominant eigenvalues.

scholarly journals Practical data correlation of flashpoints of binary mixtures by a reciprocal function: The concept and numerical examples

2011 ◽  
Vol 15 (3) ◽  
pp. 905-910 ◽  
Author(s):  
Mariana Hristova ◽  
Dimitar Damgaliev ◽  
Jordan Hristov
Keyword(s):  
Binary Mixture ◽  
Binary Mixtures ◽  
Alcohol Solution ◽  
Aqueous Alcohol ◽  
Thermodynamic Models ◽  
Data Correlation ◽  
Numerical Examples ◽  
Aqueous Alcohol Solution ◽  
Better Than

Simple data correlation of flashpoint data of binary mixture has been developed on a basic of rational reciprocal function. The new approximation requires has only two coefficients and needs the flashpoint temperature of the pure flammable component to be known. The approximation has been tested by literature data concerning aqueous-alcohol solution and compared to calculations performed by several thermodynamic models predicting flashpoint temperatures. The suggested approximation provides accuracy comparable and to some extent better than that of the thermodynamic methods.

A Note on Pseudodynamic Cost Limit Replacement Model

1998 ◽  
Vol 05 (03) ◽  
pp. 287-292 ◽  
Author(s):  
Chung Hyeon Choi ◽  
Won Young Yun
Keyword(s):  
Replacement Policy ◽  
Repair Cost ◽  
Numerical Examples ◽  
Cost Rate ◽  
Replacement Model ◽  
Mean Cost ◽  
Cost Limit ◽  
Better Than

In this note, a pseudodynamic cost limit replacement policy presented by Park1 is considered. Park1 showed that the pseudodynamic policy is inferior to constant repair cost limit policy. In this note, the correct mean cost rate under the same assumption in the Park's model is obtained and the pseudodynamic policy is shown to be better than the constant repair cost limit policy2 through the same numerical examples of Park.1

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