Singular value inclusion sets of rectangular tensors

2019 ◽  
Vol 576 ◽  
pp. 181-199 ◽  
Author(s):  
Hongmei Yao ◽  
Can Zhang ◽  
Lei Liu ◽  
Jiang Zhou ◽  
Changjiang Bu
Keyword(s):  
Singular Value ◽  
Rectangular Tensors

THE RATE OF CONVERGENCE AND WEAKER CONVERGENT CONDITION FOR THE METHOD FOR FINDING THE LARGEST SINGULAR VALUE OF RECTANGULAR TENSORS

2016 ◽  
Vol 78 (6-5) ◽  
Author(s):  
Nur Fadhilah Ibrahim ◽  
Nurul Akmal Mohamed
Keyword(s):  
Quantum Physics ◽  
Solid Mechanics ◽  
Linear Convergence ◽  
Singular Value ◽  
Strong Ellipticity ◽  
Ellipticity Condition ◽  
Condition Problem ◽  
Strong Ellipticity Condition ◽  
Weak Irreducibility ◽  
Rectangular Tensors

The applications of real rectangular tensors, among others, including the strong ellipticity condition problem within solid mechanics, and the entanglement problem within quantum physics. A method was suggested by Zhou, Caccetta and Qi in 2013, as a means of calculating the largest singular value of a nonnegative rectangular tensor. In this paper, we show that the method converges under weak irreducibility condition, and that it has a Q-linear convergence.   

scholarly journals An S-type upper bound for the largest singular value of nonnegative rectangular tensors

2016 ◽  
Vol 14 (1) ◽  
pp. 925-933 ◽  
Author(s):  
Jianxing Zhao ◽  
Caili Sang
Keyword(s):  
Upper Bound ◽  
Singular Value ◽  
Numerical Examples ◽  
Rectangular Tensors ◽  
Theoretical Results

AbstractAn S-type upper bound for the largest singular value of a nonnegative rectangular tensor is given by breaking N = {1, 2, … n} into disjoint subsets S and its complement. It is shown that the new upper bound is smaller than that provided by Yang and Yang (2011). Numerical examples are given to verify the theoretical results.

scholarly journals Bound for the largest singular value of nonnegative rectangular tensors

2016 ◽  
Vol 14 (1) ◽  
pp. 761-766 ◽  
Author(s):  
Jun He ◽  
Yan-Min Liu ◽  
Hua Ke ◽  
Jun-Kang Tian ◽  
Xiang Li
Keyword(s):  
Singular Values ◽  
Singular Value ◽  
Rectangular Tensors

AbstractIn 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.

Singular value inclusion sets for rectangular tensors

2017 ◽  
Vol 66 (7) ◽  
pp. 1333-1350 ◽  
Author(s):  
Jianxing Zhao ◽  
Chaoqian Li
Keyword(s):  
Singular Value ◽  
Rectangular Tensors
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