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[1]
L. Qi,"Eigenvalues
of a real supersymmetric tensor", Journal of
Symbolic Computation 40 (2005) 1302-1324.
[2]
L. Qi,"Rank
and eigenvalues of a supersymmetric tensor, the multivariate
homogeneous polynomial and the algebraic hypersurface it
defines", Journal of Symbolic Computation 41 (2006)
1309-1327.
[3]
L. Qi, "Eigenvalues
and invariants of tensors", Journal of Mathematical
Analysis & Applications 325 (2007) 1363-1377.
[4]
G. Ni, L. Qi, F. Wang and Y.
Wang, "The
degree of the E-characteristic polynomial of an even order
tensor", Journal of Mathematical Analysis
& Applications 329 (2007) 1218-1229.
[5]
Y. Wang and L. Qi, "On
the successive supersymmetric rank-1 decomposition of higher
order supersymmetric tensors", Numerical Linear Algebra
with Applications 14 (2007) 503-519.
[6] L. Qi, W. Sun and Y. Wang,
"Numerical
multilinear algebra and its applications", Frontiers of
Mathematics in China 2 (2007) 501-526.
[7] Q. Ni, L. Qi and F. Wang, "An
eigenvalue method for the positive definiteness identification
problem", IEEE Transactions on Automatic Control 53
(2008) 1096-1107.
[8] L. Qi, F. Wang and Y. Wang,
"Z-eigenvalue
methods for a global polynomial optimization problem",
Mathematical Programming 118 (2009) 301-316.
[9] Y.Wang, L. Qi and X. Zhang,
"A
Practical method for computing the largest M-eigenvalue of a
fourth-order partially symmetric tensor", Numerical Linear
Algebra and Applications
16 (2009) 589-601.
[10]
D. Han and L. Qi, "A
successive approximation method for quantum separability",
February 2009.
[11] K.C. Chang, L. Qi and
G. Zhou, "Singular values of a real rectangular tensor",
Journal of Mathematical Analysis &
Applications 370 (2010) 284-294.
[12] G.
Li, L. Qi and G. Yu, "Semismoothness of
the maximum eigenvalue function of a symmetric tensor and
its application'', Linear Algebra and Its Applications
438 (2013) 813-833.
B. Survey
[13] L.
Qi, W. Sun and Y. Wang, "Numerical multilinear algebra and
its applications'', Frontiers of Mathematics in China 2
(2007) 501-526.
[14] L.
Qi, "The spectral theory of tensors (rough version)",
arXiv:1201.3424v1 [math.SP] 17 Jan 2012.
C. Applications in
Biomedical Engineering
[15] L. Qi, Y. Wang
and E.X. Wu, "D-eigenvalues
of diffusion kurtosis tensors", Journal of Computational
and Applied Mathematics 221 (2008) 150-157.
[16] E.S. Hui, M.M. Cheung, L. Qi
and E.X. Wu, "Towards
better MR characterization of neural tissues using directional
diffusion kurtosis analysis", Neuroimage 42 (2008)
122-134.
[17] L. Qi, D. Han and E.X. Wu, "Principal
invariants and inherent parameters of diffusion kurtosis
tensors", Journal of Mathematical Analysis and
Applications 349 (2009) 165-180.
[18]
D. Han, L. Qi and E.X. Wu,
"Extreme
diffusion values for non-Gaussian diffusions",
Optimization Methods and Software 23 (2008) 703-716.
[19]
E.S. Hui, M.M. Cheung, L. Qi
and E.X. Wu, "Advanced
MR diffusion characterization of neural tissue using
directional diffusion kurtosis analysis", Conf. Proc. IEEE
Eng. Med. Biol.
Soc. 2008 (2008) 3941-3944.
[20] M.M. Cheung, E.S Hui, K.C Chan,
J.A Helpern, L. Qi and E.X Wu: "Does
diffusion kurtosis imaging lead to better neural tissue
characterization? A rat brain maturation study",
Neuroimage 45 (2009) 386-392.
[21]
X. Zhang, C. Ling, L. Qi and
E.X. Wu,
"The
measure of diffusion skewness and kurtosis in magnetic
resonance imaging", Pacific Journal of
Optimization 6 (2010)391-404.
[22]
L. Qi, G. Yu and E.X. Wu,
"Higher order positive semi-definite diffusion tensor
imaging",
SIAM Journal on Imaging Sciences 3 (2010) 416-433.
[23] S.L.
Hu, Z.H. Huang, H.Y. Ni and L. Qi,
"Positive definiteness of diffusion kurtosis imaging'',
to appear in: Inverse Problems and Imaging.
[24] L.
Qi, G. Yu and Y. Xu, "Nonnegative
diffusion orientation distribution function'', Journal
of Mathematical Imaging and Vision 45 (2013) 103-113.
D. Applications in Solid
Mechanics
[25] L. Qi, H.H. Dai and D.
Han. "Conditions
for strong ellipticity and M-eigenvalues", Frontiers of
Mathematics in China
4 (2009) 349-364.
[26] D. Han, H.H. Dai and
L. Qi, "Conditions
for strong ellipticity of anisotropic elastic materials",
Journal of Elasticity 97 (2009) 1-13.
E. Nonnegative
Tensors
[27]
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.
[28] 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
[29]
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.
[30] 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.
[31] 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.
[32] L.
Zhang, L. Qi, Z. Luo and Y. Xu, "The
dominant eigenvalue of an essentially nonnegative tensor'',
arXiv: 1110.6261v1 [math.NA] 28 Oct 2011, Revised in January
2013. Matlab Code of the Algorithm in
this paper.
[33] S.
Hu, Z.H. Huang and L. Qi, "Finding the
spectral radius of a nonnegative tensor", arXiv:
1111.2138v1 [math.NA] 9 Nov 2011.
[34] L.
Qi and Q. Yang,
"Eigenvalues of
nonnegative tensors", January 9, 2012.
F. Spectral Hypergraph
Theory
[35] S.
Hu and L. Qi, "Algebraic connectivity of an
even uniform hypergraph",
Journal of Combinatorial Optimization 24 (2012) 564-579.
G. Further Theory on Eigenvalues
of Tensors
[36] L. Qi,
"The
Best Rank-One Approximation Ratio of a Tensor Space'',
SIAM Journal on Matrix Analysis and
Applications 32 (2011) 430-442.
[37]
X. Zhang, C. Ling and L. Qi, "The best rank-1 approximation
of a symmetric tensor and related spherical optimization
problems'', SIAM Journal on Matrix Analysis and Applications
33 (2012) 806-821.
[38] Y.
Song and L. Qi, "The existence and uniqueness of eigenvalue
for monotone homogeneous mapping pairs'', Nonlinear Analysis
75 (2012) 5283-5293.
[39] A.M.
Li, L. Qi and B. Zhang, "E-characteristic polynomials of
tensors'', Communications in Mathematical Sciences 11 (2013)
33-53.
[40] S.
Hu and L. Qi, "E-characteristic polynomial of a tensor of
dimension two'', Applied Mathematics Letters 26 (2013)
225-231.
[41] S.
Hu, Z. Huang, C. Ling and L. Qi, "On
Determinants and Eigenvalue Theory of Tensors'', Journal
of Symbolic Computation 50 (2013) 508-531.
[42] Y.
Song and L. Qi, "Positive eigenvalue-eigenvector of
nonlinear positive mappings'', to appear in: Frontiers of
Mathematics in China.
[43] C.
Ling and L. Qi, "On
lk-singular values and spectral radius
of rectangular tensors'', Frontiers of
Mathematics in China 8 (2013) 63-84.
H. Computational Polynomial
Optimization
[44] C. Ling, J. Nie, L. Qi and Y.
Ye,
"Bi-quadratic
optimization over unit spheres and semidefinite programming
relaxations", SIAM Journal on
Optimization 20 (2009) 1286-1310.
[45] X.
Zhang, L. Qi and Y. Ye, "The cubic spherical optimization
problems'', Mathematics of
Computation 81 (2012)
1513-1525.
[46] X.
Zhang, C. Ling and L. Qi, "Semidefinite
relaxation bounds for bi-quadratic optimization problems
with quadratic constraints'', Journal of Global
Optimization 49 (2011) 293-311.
[47] C.
Ling, X. Zhang and L. Qi, "Semidefinite
relaxation approximation for multivariate bi-quadratic
optimization with quadratic constraints", Numerical
Linear Algebra with Applications 19 (2012) 113-131.
[48] I.M.
Bomze, C. Ling, L. Qi and X. Zhang, "Standard bi-quadratic
optimization problems and unconstrained polynomial
reformulations'', Journal of Global Optimization 52 (2012)
663-687.
[W1]
Workshop
of Computational Polynomial Optimization and Multilinear
Algebra
I. Space Tensor Conic
Programming
[49] L. Qi and Y. Ye,
"Space tensor conic
programming", June 2009.
J. Quantum Physics
[50] L.
Qi, "The minimum Hartree value for the quantum entanglement
problem'',
arXiv:1202.2983v1 [quant-ph] 14 Feb 2012.
K. Tensor Decomposition
[51] Y.
Chen, D. Han and L. Qi, "New ALS methods with extrapolating
search directions and optimal step size for complex-valued
tensor decompositions'', IEEE Transactions on
Signal Processing 59 (2011) 5888-5898.
L. Articles and
Photo
[P1]
Article 1 ––
四十二年后再登东嶽泰山.
[P2]
Photo –– 一覽众山小..
[P3]
Article 2
––
张量研究的两点心得.
[P4]
Article 3
––
开拓应用数学和计算数学的新疆土.
M. Special Issues: Call-of-Papers
[S1] NLA
Special Issue:
The Spectral Theory of Tensors and Its Applications
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