Structured Tensor

 

A.   Nonnegative Tensors
   
[1] M. Ng, L. Qi and G. Zhou, "Finding the largest eigenvalue of a non-negative tensor'', SIAM Journal on Matrix Analysis and Applications 31 (2009) 1090-1099.
   
[2] L. Zhang and L. Qi, "Linear convergence of an algorithm for computing the largest eigenvalue of a nonnegative tensor'', Numerical Linear Algebra with Applications 19 (2012) 830-841.
   
[3] L. Zhang, L. Qi and Y. Xu, "Linear convergence of the LZI algorithm for weakly positive tensors'', Journal of Computational Mathematics 30 (2012) 24-33.
   
[4] G. Zhou, L. Caccetta and L. Qi, "Convergence of an algorithm for the largest singular value of a nonnegative rectangular tensor'', Linear Algebra and Its Applications 438 (2013) 959-968.
   
[5] G. Zhou, L. Qi and S.Y. Wu, "Efficient algorithms for computing the largest eigenvalue of a nonnegative tensor'', Frontiers of Mathematics in China 8 (2013) 155-168.
   
[6]  G. Zhou, L. Qi and S.Y. Wu, "On the largest eigenvalue of a symmetric nonnegative tensor'', Numerical Linear Algebra with Applications 20 (2013) 913-928.
   
[7] S. Hu, Z.H. Huang and L. Qi, "Strictly nonnegative tensors and nonnegative tensor partition'', Science China Mathematics 57 (2014) 181-195.
   
[8] K.C. Chang, L. Qi and T. Zhang, "A survey on the spectral theory of nonnegative tensors'', Numerical Linear Algebra with Applications 20 (2013) 891-912.
   
[9] Z. Chen, L. Qi, Q. Yang and Y. Yang, "The solution methods for the largest eigenvalue (singular value) of nonnegative tensors and convergence analysis'', Linear Algebra and Its Applications 439 (2013) 3713-3733.
   
[10] Q. Ni and L. Qi, "A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map'', Journal of Global Optimization, 61 (2015) 627-641.
   
[11] S. Hu and L. Qi, "A necessary and sufficient condition for existence of a positive Perron vector'', SIAM Journal on Matrix Analysis and Applications 37 (2016) 1747-1770.
B.   Essentially Nonnegative Tensors
   
[12] L. Zhang, L. Qi, Z. Luo and Y. Xu, "The dominant eigenvalue of an essentially nonnegative tensor'', Numerical Linear Algebra with Applications 20 (2013) 929-941.
   
[13] S. Hu, G. Li, L. Qi and Y. Song, "Finding the maximum eigenvalue of essentially nonnegative symmetric tensors via sum of squares programming'',  Journal of Optimization Theory and Applications 158 (2013) 717-738.
   
C.   Copositive Tensors
   
[14] L. Qi, "Symmetric nonnegative tensors and copositive tensors'', Linear Algebra and Its Applications 439 (2013) 228-238.
   
[15] Y. Song and L. Qi, "Necessary and sufficient conditions for copositive tensors'', Linear and Multilinear Algebra 63 (2015) 120-131.
   
D.   Z-Tensors, M-Tensors and H-Tensors
   
[16] L. Zhang, L. Qi and G. Zhou, "M-tensors and and some applications", SIAM Journal on Matrix Analysis and Applications 35 (2014) 437-452.
   
[17] W. Ding, L. Qi and Y. Wei, "M-tensors and nonsingular M-tensors'', Linear Algebra and Its Applications 439 (2013) 3264-3278.
   
[18] H. Chen and L. Qi, "Some spectral properties of odd-bipartite Z-tensors and their absolute tensors'', Frontiers of Mathematics in China 11 (2016) 539-556.
   
[19]

Y. Li, Q. Liu and L. Qi, "Programmable criteria for strong H-tensorss'', Numerical Algorithms, 74 (2017) 199-221.
   
E.   Completely Positive Tensors
   
[20] L. Qi, C. Xu and Y. Xu, "Nonnegative tensor factorization, completely positive tensors and an Hierarchically elimination algorithm'',  SIAM Journal on Matrix Analysis and Applications 35 (2014) 1227-1241.
   
[21] Z. Luo and L. Qi, "Completely positive tensors: Properties, easily checkable subclasses and tractable relaxations'', SIAM Journal on Matrix Analysis and Applications 37 (2016) 1675-1698.
   
[22] C. Xu, Z. Luo, L. Qi and Z. Chen "{0, 1} Completely Positive Tensors and Multi-Hypergraphs'', Linear Algebra and Its Applications 510 (2016) 110-123.
   
F.   Hankel Tensors
   
[23] L. Qi, "Hankel tensors: Associated Hankel matrices and Vandermonde decomposition'', Communications in Mathematical Sciences 13 (2015) 113-125.
   
[24] W. Ding, L. Qi and Y. Wei, "Fast Hankel tensor-vector products and application to exponential data fitting",  Numerical Linear Algebra with Applications 22 (2015) 814-832.
   
[25] G. Li, L. Qi and Y. Xu, "SOS Hankel Tensors: Theory and Application'', October 2014,  arXiv:1410.6989.
   
[26] Q. Wang, G. Li, L. Qi and Y. Xu, "New classes of positive semi-definite Hankel tensor", Minimax and Its Applications 2 (2017).
   
[27] G. Li, L. Qi and Q. Wang, "Positive semi-definiteness of generalized anti-circular tensors'', Communications in Mathematical Sciences 14 (2016) 941-952.
   
[28] Y. Chen, L. Qi and Q. Wang, "Computing extreme eigenvalues of large scale Hankel tensors", Journal of Scientific Computing, 68 (2016) 716-738. 
   
[29] Y. Chen, L. Qi and Q. Wang, “Positive semi-definiteness and sum-of-squares property of fourth order four dimensional Hankel tensors”, Journal of Computational and Applied Mathematics, 302 (2016) 356-368.
   
[30] W. Ding, L. Qi and Y. Wei, “Inheritance properties and sum-of-squares decomposition of Hankel tensors: Theory and algorithm”, BIT Numerical Mathematics 57 (2017) 169-190.
   
G.   Cauchy Tensors and Hilbert Tensors
   
[31]  Y. Song and L. Qi, "Infinite and finite dimensional Hilbert Tensors", Linear Algebra and Its Applications 451 (2014) 1-14.
   
[32] H. Chen and L. Qi, "Positive definiteness and semi-definiteness of even order symmetric Cauchy tensors'',  Journal of Industrial and Management Optimization 11 (2015) 1263-1274.
   
[33] H. Chen, G. Li and L. Qi, "Further results on Cauchy tensors and Hankel tensors'', Applied Mathematics and Computation 275 (2016) 50-62.
   
H.   Toeplitz Tensors
   
[34] Z. Chen and  L. Qi, "Circulant Tensors with Applications to Spectral Hypergraph Theory and Stochastic Process'', Journal of Industrial and Management Optimization 12 (2016) 1227-1247.
   
[35] L. Qi, Q. Wang and Y. Chen, "Three dimensional strongly symmetric circulant tensors'', Linear Algebra and Its Applications 482 (2015) 207-220.
   
I.   P, Q and B Tensors
   
[36] Y. Song and L. Qi, "Properties of some classes of structured tensors'', to appear in: Journal of Optimization: Theory and Applications,  arXiv:1403.1118
   
[37] L. Qi and Y. Song, "An even order symmetric B tensor is positive definite", Linear Algebra and Its Applications 457 (2014) 303-312.
   
[38] C. Li, L. Qi and Y. Li, "MB-tensors and MB_0-tensors'', Linear Algebra and Its Applications 484  (2015) 141-153.
   
[39] Y. Song and L. Qi, "Property of tensor complementarity problem and some classes of structured tensors'', November 2014.  arXiv:1412.0113.
   
J.   Centrosymmetric and Skew Centrosymmetric Tensors
   
[40] H. Chen, Z. Chen and L. Qi, "Centrosymmetric, skew centrosymmetric and centrosymmetric Cauchy Tensors'', June 2014.   arXiv:1406.7409.
   
K.   Positive Semi-Definite Tensors and SOS Tensors
   
[41] S. Hu, G. Li and L. Qi, "A tensor analogy of Yuan's alternative theorem and polynomial optimization with sign structure'', Journal of Optimization Theory and Applications, 168 (2016) 446-474.
   
[42] Z. Luo, L. Qi and Y. Ye, "Linear operators and positive semidefiniteness of symmetric tensor spaces'', Science China Mathematics, 58 (2015) 197-212.
   
[43] H. Chen, G. Li and L. Qi, "SOS Tensor Decomposition: Theory and Applications", Communications in Mathematical Sciences 14 (2016) 2073-2100.
   
[44] Z. Luo and L. Qi, "Positive Semidefinite Tensors" (in Chinese), Science China Mathematics 46 (2016) 639-654.
   
L.   Mode-Symmetric Tensors
   
[45] M. Che, L. Qi and Y. Wei, "Perturbation bounds for tensor eigenvalues and singular values problems'', Linear and Multilinear Algebra 64 (2016) 622-652.
   
[46] X. Zhang, Z. Huang and L. Qi, "Comon's Conjecture, rank decomposition and symmetric rank decomposition of symmetric tensors'',  SIAM Journal on Matrix Analysis and Applications 37 (2016) 1719-1728.