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[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.
B.
Essentially
Nonnegative Tensors
[11]
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.
[12]
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
[13]
L. Qi,
"Symmetric nonnegative tensors and
copositive tensors'', Linear Algebra and
Its Applications 439 (2013) 228-238.
[14]
Y. Song and L. Qi,
"Necessary and sufficient conditions for
copositive tensors'', Linear and
Multilinear Algebra 63 (2015) 120-131.
D.
Z-Tensors
and M-Tensors
[15]
L.
Zhang, L. Qi and G. Zhou,
"M-tensors and and some applications",
SIAM Journal on Matrix Analysis and
Applications 35 (2014) 437-452.
[16]
W. Ding, L. Qi and Y. Wei,
"M-tensors and nonsingular M-tensors'',
Linear Algebra and Its Applications 439
(2013) 3264-3278.
[17] H. Chen and L. Qi,
"Some spectral properties of odd-bipartite
Z-tensors and their absolute tensors",
to appear in: Frontiers of Mathematics in
China.
E.
Completely
Positive Tensors
[18]
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.
F.
Hankel Tensors
[19]
L. Qi,
"Hankel tensors: Associated Hankel matrices
and Vandermonde decomposition'',
Communications in Mathematical Sciences 13
(2015) 113-125.
[20]
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.
[21]
G.
Li, L. Qi and Y. Xu,
"SOS Hankel Tensors: Theory and
Application'', October 2014,
arXiv:1410.6989.
[22]
G.
Li, L. Qi and Q. Wang,
"Are there sixth order three dimensional
Hankel tensors?'', November 2014.
arXiv:1411.2368.
[23]
G.
Li, L. Qi and Q. Wang,
"Positive semi-definiteness of generalized
anti-circular tensors'',
to appear in: Communications in Mathematical
Sciences.
[24]
Y. Chen,
L. Qi and Q. Wang,
"Computing extreme eigenvalues of large
scale Hankel tensors", Journal of
Scientific Computing,
DOI:10.1007/s10915-015-0155-8 (2016).
[25]
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, doi:10.1016/
j.cam.2016.02.019 (2016).
G.
Cauchy Tensors and HilbertTensors
[26]
Y. Song and L. Qi,
"Infinite and finite dimensional Hilbert
Tensors", Linear Algebra and Its
Applications 451 (2014) 1-14.
[27]
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.
[28]
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
[29]
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.
[30]
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
[31]
Y. Song and L. Qi,
"Properties of some classes of structured
tensors'', to appear in: Journal of
Optimization: Theory and Applications,
arXiv:1403.1118
[32]
L. Qi and Y. Song,
"An even order symmetric B tensor is
positive definite",
Linear Algebra and Its
Applications 457 (2014) 303-312.
[33]
C. Li, L. Qi and Y. Li,
"MB-tensors and MB_0-tensors'', Linear
Algebra and Its Applications 484 (2015)
141-153.
[34]
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
[35]
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
[36]
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.
[37]
Z. Luo, L. Qi and Y. Ye,
"Linear operators and positive
semidefiniteness of symmetric tensor
spaces'', Science China Mathematics, 58
(2015) 197-212.
[38] H. Chen, G. Li and L. Qi,
"SOS Tensor Decomposition: Theory and
Applications", to appear in: Communications in Mathematical Sciences.
L. Mode-Symmetric
Tensors
[39] M. Che, L. Qi and Y. Wei,
"Perturbation bounds for tensor eigenvalues
and singular values problems'', to
appear in: Linear and Multilinear Algebra.
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