Tiexiang Li

Visiting Scholar

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Research Fields: Matrix Computations, Metric-Preserving Computational Geometry, Data Science, Image Processing
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Bio

Tiexiang Li is a Professor of Mathematics at Southeast University and also serves as a professor and assistant director at Shing-Tung Yau Center of Southeast University and Nanjing Center for Applied Mathematics. She obtained her Ph.D in mathematics at Peking University in 2008.

Professor Li’s research interests include matrix computations, 3D metric-preserving computational geometry, inverse problems, data science, image processing, deep learning. She has published over 60 papers in leading journals, including SIAM J. Sci. Comput., SIAM J. Matrix Anal.Appl., SIAM J. Imaging Sci., J. Comput. Phys., Inverse Probl., J. Differ. Equ., ACM T. Math. Software, Comput. Phys. Commun..

Education Experience

  • 2003.9 – 2008.1  Peking University Mathematics Doctor
  • 1999.9 – 2003.7  East China Normal University Mathematics B.S.

Work Experience

  • 2019.4 – Southeast University Professor
  • 2012.4 – 2019.4 Southeast University Associate Professor
  • 2008.4 – 2012.4 Southeast University Assistant Professor
  • 2009.2 – 2010.1 Taiwan Yang Ming Chiao Tung University Postdoctoral

Honors and Awards

  • 2021: First Prize of the Huaxia Construction Science and Technology Award (Ranked 5th)
  • 2020: Youth Award in Industrial and Applied Mathematics from the Third Jiangsu Society for Industrial and Applied Mathematics
  • 2019: World Chinese Mathematician Union Best Paper Award – Ruolin Prize
  • 2017: World Chinese Mathematician Union Best Paper Award – Ruolin Prize
  • 2014: Candidate for the Young Academic Leader of Jiangsu Province’s “Qing Lan Project”
  • 2012: Third Prize of the Jiangsu Science and Technology Award (Ranked 5th)

Publications

  1. Q. Liu, H.-N. Yang, T. Li, H. Tian and Z. Yang, An efficient and unified method for band structure calculations of 2D anisotropic photonic-crystal fibers, Calcolo, 2024, accepted.
  2. X.L. Lyu, H. Tian, T. Li and W.W. Lin, Fast SVD-Based Linear Elastic Eigenvalue Problem Solver for Band Structures of 3D Phononic Crystals, Journal of Scientific Computing, 2024, accepted.
  3. H. Liu, Z. Li, K. Huang, Rui Wang, G. Cheng and T. Li,  Evolutionary Reinforcement Learning Algorithm for Large‑scale Multi‑agent Cooperation and Confrontation Applications, The Journal of Supercomputing, 2023.
  4. 杨浩楠，吕星龙，李铁香，杨占山，三维各向异性光子晶体的快速仿真算法，东南大学学报（自然科学版）, 2023, Vol. 53(4), 725—732.
  5. J.-W. Liao, T.-M. Huang, T. Li, W.-W. Lin, H. Wang and S.-T. Yau, An UNet-Based Brain Tumor Segmentation Framework via Optimal Mass Transportation Pre-processing, In: Bakas, S., et al. Brainlesion: Glioma, Multiple Sclerosis, Stroke and Traumatic Brain Injuries. BrainLes 2022. Lecture Notes in Computer Science, 2023, Vol. 13769. Springer, Cham.
  6. H. Tian, T. Li, X.-L. Lyu and W.-W. Lin, Band Structure Calculations of Three-dimensional Anisotropic Photonic Crystals in the Oblique Coordinate System, SIAM Journal on Scientific Computing, 2023, 45(4), B440–B466.
  7. J.-W. Lin, T. Li, W.-W. Lin and T.-M. Huang, Ellipsoidal Conformal and Area-/Volume-Preserving Parameterizations and Associated Optimal Mass Transportations, Advances in Computational Mathematics, 2023, 49, 50.
  8. Q. Liu, T. Li and S. Zhang, A Mixed Element Scheme for the Helmholtz Transmission Eigenvalue Problem for Anisotropic Media, Inverse Problems, 2023, 39, 055005.
  9. W.-W. Lin, T. Li, T.-M. Huang, J.-W. Lin, M.-H. Yueh and S.-T. Yau, A Two-Phase Optimal Mass Transportation Technique for 3D Brain Tumor Detection and Segmentation, In: Crimi, A., Bakas, S. (eds) Brainlesion: Glioma, Multiple Sclerosis, Stroke and Traumatic Brain Injuries. BrainLes 2021. Lecture Notes in Computer Science, 2022, 12962, 400–409, Springer, Cham.
  10. W.-W. Lin, J.-W. Lin, T.-M. Huang, T. Li, M.-H. Yueh and S.-T. Yau, A Novel 2-Phase Residual U-Net Algorithm Combined with Optimal Mass Transportation for 3D Brain Tumor Detection and Segmentation, Scientific Reports, 2022, 12, 6452.
  11. T. Li, P.-S. Chuang and M.-H. Yueh, An Optimal Transportation-Based Recognition Algorithm for 3D Facial Expressions, Annals of Mathematical Sciences and Applications, 2022, 7(1), 49–96.
  12. X.-L. Lyu, T. Li, J.-W. Lin, T.-M. Huang, W.-W. Lin and H. Tian, Solving Maxwell Eigenvalue Problems for Three Dimensional Isotropic Photonic Crystals with Fourteen Bravais Lattices, Journal of Computational and Applied Mathematics, 2022, 410, 114220.
  13. X. Liang, Z.-C. Guo, T.-M. Huang, T. Li and W.-W. Lin, Bifurcation Analysis of the Eigenstructure of the Discrete Single-Curl Operator in Three-Dimensional Maxwell’s Equations with Pasteur Media, IMA Journal of Numerical Analysis, 2022, 42(4), 3735–3770.
  14. W.-W. Lin, C. Juang, M.-H. Yueh, T.-M. Huang, T. Li, S. Wang and S.-T. Yau, 3D Brain Tumor Segmentation Using a Two-Stage Optimal Mass Transport Algorithm, Scientific Reports, 2021, 11, 14686.
  15. M.-H. Yueh, T.-M. Huang, T. Li, W.-W. Lin and S.-T. Yau, Projected Gradient Method Combined with Homotopy Techniques for Volume-Measure-Preserving Optimal Mass Transportation Problems, Journal of Scientific Computing, 2021, 88(3), 64.
  16. W.-C. Chang, T. Li, W.-W. Lin and J.-N. Wang, Computation of the Interior Transmission Eigenvalues for Elastic Scattering in an Inhomogeneous Medium Containing an Obstacle, Research in the Mathematical Sciences, 2021, 8(3), 49.
  17. H. Tian, X.-L. Lyu and T. Li, A Structure-Preserving Method for Solving the Complex ⊤-Hamiltonian Eigenvalue Problem, Annals of Mathematical Sciences and Applications, 2021, 6(2), 199–224.
  18. T. Li, W.-W. Lin, Y. Wang and S.-T. Yau, Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices, Analysis in Theory and Applications, 2021, 37(4), 481–519.
  19. X.-L. Lyu, T. Li, T.-M. Huang, J.-W. Lin, W.-W. Lin and S. Wang, FAME: Fast Algorithms for Maxwell’s Equations for Three-Dimensional Photonic Crystals, ACM Transactions on Mathematical Software, 2021, 47(3), 26.
  20. X.-L. Lyu, T. Li, T.-M. Huang, W.-W. Lin and H. Tian, The Bi-Lebedev Scheme for the Maxwell Eigenvalue Problem with 3D Bi-Anisotropic Complex Media, Computer Physics Communications, 2021, 261, 107769.
  21. X.-L. Lyu, T. Li and E.K.-W. Chu, Solving Large-Scale Discrete-Time Algebraic Riccati Equations by Doubling, Proceedings of the 32nd Chinese Control and Decision Conference, CCDC 2020, 4507–4512.
  22. M.-H. Yueh, T. Li, W.-W. Lin and S.-T. Yau, A New Efficient Algorithm for Volume-Preserving Parameterizations of Genus-One 3-Manifolds, SIAM Journal on Imaging Sciences, 2020, 13(3), 1536–1564.
  23. H.-S. Zhang, T. Li and T.-F. Wu, On the Solvability of an Indefinite Nonlinear Kirchhoff Equation via Associated Eigenvalue Problems, Journal of Differential Equations, 2020, 269, 2853–2895.
  24. T.-M. Huang, T. Li, J.-W. Lin, W.-W. Lin and H. Tian, Structure-Preserving Methods for Computing Complex Band Structures of Three Dimensional Photonic Crystals, Journal of Scientific Computing, 2020, 83(2), 35.
  25. M.-H. Yueh, H.-H. Huang, T. Li, W.-W. Lin, and S.-T. Yau, Optimized Surface Parameterizations with Applications to Chinese Virtual Broadcasting, Electronic Transactions on Numerical Analysis, 2020, 53, 383–405.
  26. H.-S. Zhang, T. Li and T.-F. Wu, Existence and Multiplicity of Nontrivial Solutions for Biharmonic Equations with Singular Weight Functions, Applied Mathematics Letters, 2020, 105, 106335.
  27. 葛安同, 谢晓慧, 谭忠恒, 李铁香, 张云, 黄睿. 基于多尺度特征提取的电力客户欠费风险预测. 电力工程技术, 2020, 39, 159–165．
  28. M.-H. Yueh, T. Li, W.-W. Lin and S.-T. Yau, A Novel Algorithm for Volume-Preserving Parameterizations of 3-Manifolds, SIAM Journal on Imaging Sciences, 2019, 12(2), 1071–1098.
  29. S.-H. Chou, T.-M. Huang, T. Li, J.-W. Lin and W.-W. Lin, A Finite Element Based Fast Eigensolver for Three Dimensional Anisotropic Photonic Crystals, Journal of Computational Physics, 2019, 386, 611–631.
  30. T.-M. Huang, T. Li, R.-L. Chern and W.-W. Lin, Electromagnetic Field Behavior of 3D Maxwell’s Equations for Chiral Media, Journal of Computational Physics, 2019, 379, 118–131.
  31. Z.-C. Guo, T. Li, Y.-Y. Zhou, Structure-Preserving ΓQR and Γ-Lanczos Algorithms for Bethe-Salpeter Eigenvalue Problems, Journal of Computational and Applied Mathematics, 2018, 341, 12–30.
  32. T. Li, T.-M. Huang, W.-W. Lin and J.-N. Wang, On the Transmission Eigenvalue Problem for the Acoustic Equation with a Negative Index of Refraction and a Practical Numerical Reconstruction Method, Inverse Problems & Imaging, 2018, 12(4), 1033–1054.
  33. T. Li, T.-M. Huang, W.-W. Lin and J.-N. Wang, An Efficient Numerical Algorithm for Computing Densely Distributed Positive Interior Transmission Eigenvalues, Inverse Problems, 2017, 33, 035009.
  34. T. Li, R.-C. Li and W.-W. Lin, A Symmetric Structure-Preserving ΓQR Algorithm for Linear Response Eigenvalue Problems, Linear Algebra and its Applications, 2017, 520, 191–214.
  35. X. Zhou and T. Li, Numerical Solution of Transmission Eigenvalue Problems of Helmholtz Equation. Advances in Applied Mathematics, 2016, 5(4), 683–694.
  36. T. Li, W.-Q. Huang, W.-W. Lin and J. Liu, On Spectral Analysis and a Novel Algorithm for Transmission Eigenvalue Problems, Journal of Scientific Computing, 2015, 64(1), 83–108.
  37. T. Li, J. Sun and T.-F. Wu, Existence of Homoclinic Solutions for a Fourth Order Differential Equation with a Parameter, Applied Mathematics and Computation, 2015, 251, 499–506.
  38. T. Li and D. Chu, A Structure-Preserving Algorithm for Semi-Stabilizing Solutions of Generalized Algebraic Riccati Equations, Electronic Transactions on Numerical Analysis, 2014, 41, 396–419.
  39. T. Li, E.K.-W. Chu, Y-C. Kuo and W.-W. Lin, Solving Large-Scale Nonsymmetric Algebraic Riccati Equations by Doubling, SIAM Journal on Matrix Analysis and Applications, 2013, 34(3), 1129–1147.
  40. T. Li, P.C.-Y. Weng, E.K.-W. Chu and W.-W. Lin, Large-Scale Stein and Lyapunov Equations, Smith Method, and Applications, Numerical Algorithms, 2013, 63, 727–752.
  41. T.-M. Huang, T. Li, W.-W. Lin and P.C.-T. Wu, Numerical Studies on Structure-Preserving Algorithms for Surface Acoustic Wave Simulations, Journal of Computational and Applied Mathematics, 2013, 244, 140–154.
  42. T. Li, E.K.-W. Chu and W.-W. Lin, Solving Large-Scale Continuous-Time Algebraic Riccati Equations by Doubling, Journal of Computational and Applied Mathematics, 2013, 237(1), 373–383.
  43. T. Li and E.K.-W. Chu, Pole Assignment for Linear and Quadratic Systems with Time-Delay in Control, Numerical Linear Algebra with Applications, 2013, 20, 291–301.
  44. W.-Q. Huang, T. Li, Y.-T. Li and W.-W. Lin, A Semiorthogonal Generalized Arnoldi Method and its Variations for Quadratic Eigenvalue Problems, Numerical Linear Algebra with Applications, 2013, 20, 259–280.
  45. M. Chang, S. Zhou, Q. Sun, T. Li and J. Ni, Recovery of Bacillus Thuringiensis Based Biopesticides from Fermented Sludge by Cross-flow Microfiltration,  Desalination and Water Treatment, 2012, 43, 17–28.  
  46. X. Yin, S. Liu and T. Li, On Positive Definite Solutions of the Matrix Equation X+AX^(−q)A=Q(0 < q <= 1), Taiwanese Journal of Mathematics, 2012, 16(4), 1391–1407. T. Li and T.-F. Wu, Existence of Multiple Positive Solutions for Nonhomogeneous Elliptic Problems in R^N, Nonlinear Analysis, Theory, Methods & Applications, 2012, 75(14), 5639–5652. E.K.-W. Chu, T. Li, W.-W. Lin and P.C-Y. Weng, A Modified Newton’s Method for Rational Riccati Equations Arising in Stochastic Control, 2011 International Conference on Communications, Computing and Control Applications (CCCA 2011), 2011. E.K.-W. Chu, T. Li and W.-W. Lin, ARE-Type Iterations for Rational Riccati Equations Arising in Stochastic Control, Proceedings of the 2011 Chinese Control and Decision Conference (CCDC), 2011. T. Li, E.K.-W. Chu and X. Zhao, Robust Pole Assignment via the Schur-Newton Algorithms, 2011 International Conference on Multimedia Technology, 2332–2335, 2011. T. Li, E.K.-W. Chu, J. Juang and W.-W. Lin, Solution of a Nonsymmetric Algebraic Riccati Equation from a Two-Dimensional Transport Model, Linear Algebra and its Applications, 2011, 434(1), 201–214. T. Li, E.K.-W. Chu, J. Juang and W.-W. Lin, Solution of a Nonsymmetric Algebraic Riccati Equation from a One-Dimensional Multistate Transport Model, IMA Journal of Numerical Analysis, 2011, 31, 1453–1467. T. Li, C.-Y. Chiang, E.K.-W. Chu and W.-W. Lin, The Palindromic Generalized Eigenvalue Problem Ax=\lambda Ax: Numerical Solution and Applications, Linear Algebra and its Applications, 2011, 434, 2269–2284.
  47. E.K.-W. Chu, H.-Y. Fan, Z. Jia, T. Li and W.-W. Lin, The Rayleigh-Ritz Method, Refinement and Arnoldi Process for Periodic Matrix Pairs, Journal of Computational and Applied Mathematics, 2011, 235(8), 2626–2639.
  48. T. Li, E.K.-W. Chu and W.-W. Lin, Robust Pole Assignment for Ordinary and Descriptor Systems via the Schur Form, Numerical Linear Algebra in Signals, Systems and Control, 2011, 80, 341–365.
  49. T. Li, E.K.-W. Chu and C.-S. Wang, Asymptotic Perturbation of Palindromic Eigenvalue Problems, Taiwanese Journal of Mathematics, 2010, 14(3A), 781–793.
  50. T. Li, E.K.-W. Chu and W.-W. Lin, A Structure-Preserving Doubling Algorithm for Quadratic Eigenvalue Problems Arising from Time-Delay Systems, Journal of Computational and Applied Mathematics, 2010, 233(8), 1733–1745.
  51. T. Li, H.-L. Lin and T.-F. Wu, Existence of 2-Nodal Solutions for Semilinear Elliptic Equations in Unbounded Domains, Advanced Nonlinear Studies, 2010, 10, 1–21.
  52. T. Li and T.-F. Wu, Multiple Positive Solutions for a Dirichlet Problem Involving Critical Sobolev Exponent, Journal of Mathematical Analysis and Applications, 2010, 369, 245–257.
  53. T. Li and E.K.-W. Chu, A Schur-Newton Algorithm for Robust Pole Assignment of Descriptor Systems, Taiwanese Journal of Mathematics, 2008, 12(7), 1805–1825.
  54. T. Li and E.K.-W. Chu, A Schur-Newton Algorithm for Robust Pole Assignment, Taiwanese Journal of Mathematics, 2007, 11(5), 1485–1502.
  55. T. Li and M. Wei, Generalization of the Frobenius Metric (Chinese), Journal of East China Normal University (Natural Sciences), 2005, 3, 6–11.
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