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(with M. M. Lin), Low dimensional polytope approximation and its applications
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Data
mining and applied linear algebra, International Conference on Informatics
Education and Research for Knowledge-Circulating Society, ICKS 2008, 20-25.
Numerical
linear algebra algorithms as dynamical systems, Acta
Numerica, 17(2008), 1-86.
(with B. Dong and M.
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partial eigeninformation, Journal of Sound and Vibration, 327(2009),
391-401.
(with M. Lin and B. Dong), Inverse mode problem for real symmetric quadratic models, Inverse Problems, 26(2010), 065003, (DOI: 10.1088/0266-5611/26/6/065003)
(with M. Lin and B.
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(with M. Lin and B.
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(with M. Lin), On the nonnegative
rank of Euclidean distance matrices, Linear Alg. Appl., 433(2010),
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(with M. Lin), Dynamical System Characterization of the Central Path and Its Variants --- A Revisit, SIAM. J. Appl. Dyn. Syst. 10(2011), 887-905.
(with L.-H. Zhang), Computing absolute maximum correlation, IMA J. Numer. Anal., 32(2012), 163-184.
(with C.-H. Kuo and M. Lin), Spline
Approximation of policy functions in Economics with Uncertainties, Computational Economics, 42(2013), 175-198, (DOI: 10.1007/s10614-012
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(with M. Lin and L.
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(with M. Lin and B.
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(with M. Lin), On the finite rank and finite dimensional representation of bounded semi-infinite hankel operators, IMA J. Numer. Anal., (DOI: 10.1093/imanum/dru001), 2014.
(with L. Wang), On the global convergence of the alternating least method for rank-one approximation to generic tensors, SIAM J. Matrix Ana. Appl., 35(2014), 1058-1072.
(with L. Wang and B. Yu), Orthogonal low-rank tensor approximation: Alternating least square method and its global convergence, SIAM J. Matrix Ana. Appl., 36(2015), 1-19.
(with S.-J. Wu), Attaining the optimal Gaussian diffusion acceleration, J. Stat. Phys., 155(2014), 571-590.
(with L. Wang and B. Yu), Gradient flow for generalized normal equation with applications to linear matrix equations, Numer. Algorithms, 68(2015), 121-141, (DOI:10.1007/s11075-014-9885-1).
(with S.-J. Wu), Constructing optimal transition matrix for Markov Chain Monte Carlo via Global Optimization, Linear Alg. Appl., 487(2015), 184-202.
Solving Nonlinear Matrix Equation $X+A^{*}X^{-1}A = Q$ Fej\'{e}r-Riesz Factorization, Linear Alg. Appl., 489(2016), 123-143.
On the dynamics of maximin flows, Preprint, 2016.
(with S.-J. Wu), Markov Chains with Memory, Tensor Formulation, and the Dynamics of Power Iteration, Applied Math. Comput., 303(2017), 226-239.
(with S.-J. Wu), Solving an inverse eigenvalue problem subject to triple constraints on diagonal elements, eigenvalues, and singular values, Inverse Problems, 33(2017), no. 8, 085003.
On the adjoint of tensors and some associated musings, Preprint, 2017.
(with L.Z. Liao), Numerical methods for gradient dynamics, Preprint, 2017.
(with Y. Guan and D. Chu), SVD-based algorithms for the best rank-1 approximation of a symmetric tensor, SIAM J. Matrix Anal. Appl., 39(2018), 1095-1115.
(with Y. Guan and D. Chu), Convergence analysis of an SVD-based algorithm for the best rank-1 tensor approximation, Linear Alg. Appl., 555(2018), 53-69.
(with N. Jiang and B. Dong), Global rank-1 approximation for order-3 tensors, preprint, 2018.
(with Y. Guan, N. Jiang, and B. Dong), A theoretical consideration of matrix-operative alternating least squares methods for orthogonal CP tensor approximation, preprint, 2018.
(with N. Jiang), Decoupling of Lattice Vibration, preprint, 2018.
(with Y. Guan, B. Dong, and N. Jiang), Convergence analysis of alternating direction methods: A general framework and its applications to tensor approximations, preprint, 2018.
(with N. Jiang and J.-H. Shen), Structure preserving isospectral transformation for total or partial decoupling of self-adjoint quadratic pencils, J. Sound Vibration, 488(2019), 157-171.
(with B. Dong and N. Jiang), Nonlinear power-like iteration by polar decomposition and its application to tensor approximation, Numer. Math., 144(2020), 729-749.
(with M. Lin), Nonlinear power-like and SVD-like iterative schemes with applications to entangled bipartite rank-1 approximation, SIAM J. Sci. Comput., 43(2021), S448-S474.
(with M. Lin), A complex-valued gradient flow for the entangled bipartite low rank approximation, Comput. Phys. Commun., 271(2022), Paper No. 108185.
(with M. Lin), Rank-1 approximation for entangled multipartite real systems, J. Sci. Comput., 91 (2022), Paper No. 24.
(with M. Lin), Low rank approximation to entangled multipartite quantum systems, Quantum Inform. Process., 21(2022), Paper No. 120.
Lax Dynamics for Cartan Decomposition with Applications to Hamiltonian Simulation, IMA J. Numer. Anal., drad018, 2023.
(with Z. Zhang), An Innate Moving Frame on Parametric Surfaces: The Dynamics of Principal Singular Curves, Mathematics, 2023, 11(15), 3306; https://doi.org/10.3390/math11153306.
(with M. Lin), On the Enumeration of
Subcells within Hypercubes and Its Application to the Borsuk-Ulam Theorem,
2024, Numerical Algorithm.
On the commutative substructure within Cartan pairs of subalgebras in , 2024, submitted.
Lax dynamics for Cartan
decomposition II: Formulation and Convergence, 2024, preprint.