BIMSA > Xin Liang
Associate Professor Xin Liang

Group: Computational Mathematics

Office: A12-103

Email: liangxin@bimsa.cn

Research Field: Numerical Algebra

Biography

Xin Liang earned a bachelor's degree and Ph.D from the School of Mathematical Sciences at Peking University in 2009 and 2014 respectively. He subsequently conducted postdoctoral research at the Max Planck Institute for Dynamics of Complex Technical Systems in Germany and the Department of Applied Mathematics at National Chiao Tung University. Once he served as an assistant professor at the Yau Mathematical Sciences Center of Tsinghua University. Since 2024 he has been working in BIMSA as an associate professor. His research lies in numerical linear algebra and matrix analysis, with achievements in areas such as theories and algorithms for eigenvalue problem and algebraic Riccati equations. He is an author of the textbook Linear Algebra Primer.

Research Interest

  • Numerical Linear Algebra
  • Matrix Analysis
  • Algebraic Eigenvalue Problems
  • Matrix Equations
  • Randomized Algorithms

Education Experience

  • 2011 - 2013      University of Texas at Arlington      Computational Mathematics      Visiting Student      (Supervisor: Prof. Ren-Cang Li)
  • 2009 - 2014      Peking University      Computational Mathematics      D.Sc.      (Supervisor: Prof. Shufang Xu)
  • 2005 - 2009      Peking University      Computational Mathematics      B.Sc.

Work Experience

  • 2024 -      Beijing Institute of Mathematical Sciences and Applications      Associate Professor
  • 2021 - 2024      Beijing Institute of Mathematical Sciences and Applications      Adjunct Assistant Professor
  • 2018 - 2024      Tsinghua University      Assistant Professor
  • 2018 - 2018      University of Texas at Arlington      Visiting Scholar
  • 2016 - 2017      National Chiao Tung University      Postdoctoral Researcher
  • 2014 - 2016      Max Planck Institute for Dynamics of Complex Technical Systems      Postdoctoral Researcher

Honors and Awards

  • 2024      Ruolin Prize
  • 2022      Ruolin Prize

Publication

  • [1] ZC Guo, X Liang, An RADI-type method for stochastic continuous-time algebraic Riccati equations, arXiv preprint arXiv:2403.02940 (2024)
  • [2] Xin Liang, and Ren-Cang Li, On Generalizing Trace Minimization Principles, II, LINEAR ALGEBRA AND ITS APPLICATIONS, 687(2024), 8-37
  • [3] X Liang, On the optimality of the Oja’s algorithm for online PCA, Statistics and Computing, 33(3), 62 (2023)
  • [4] Xin Liang, Zhen-Chen Guo, Li Wang, Ren-Cang Li, and Wen-Wei Lin, Nearly optimal stochastic approximation for online principal subspace estimation, Science China-Mathematics, 66(2023), 1087-1122
  • [5] Zhen-Chen Guo and Xin Liang, The intrinsic Toeplitz structure and its applications in algebraic Riccati equations, NUMERICAL ALGORITHMS, 93(2023), 227-267
  • [6] Xin Liang, On the optimality of the Oja's algorithm for online PCA, STATISTICS AND COMPUTING, 33(2023), e62
  • [7] Zhen-Chen Guo and Xin Liang, Stochastic algebraic Riccati equations are almost as easy as deterministic ones theoretically, SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 44(2023), 4, 1749-1770
  • [8] Xin Liang, Li Wang, Lei-Hong Zhang, and Ren-Cang Li, On generalizing trace minimization principles, LINEAR ALGEBRA AND ITS APPLICATIONS, 656(2023), 483-509
  • [9] X Liang, ZC Guo, TM Huang, T Li, WW 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, 42(4), 3735-3770 (2022)
  • [10] 梁鑫，田垠，杨一龙, 线性代数入门(2022)
  • [11] Xiaojing Jia, Xin Liang, Chungen Shen, and Lei-Hong Zhang, Solving the cubic regularization model by a nested restarting Lanczos method, SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 43(2022), 812-839
  • [12] Peter Benner, and Xin Liang, Convergence analysis of vector extended locally optimal block preconditioned extended conjugate gradient method for computing extreme eigenvalues, NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 29(2022), 6, e2445
  • [13] Huaming Ling, Chenglong Bao, Xin Liang, Zuoqiang Shi, Semi-Supervised Clustering via Dynamic Graph Structure Learning, arXiv:2209.02513(2022)
  • [14] Peter Benner, Xin Liang, Suzana Miodragović, and Ninoslav Truhar, Relative perturbation theory for quadratic Hermitian eigenvalue problems, LINEAR ALGEBRA AND ITS APPLICATIONS, 618(2021), 97-128
  • [15] Xin Liang, Note on finding an optimal deflation for quadratic matrix polynomials, CSIAM Transactions on Applied Mathematics, 2(2021), 2, 336-356
  • [16] Xin Liang and Ren-Cang Li, The hyperbolic quadratic eigenvalue problem, Forum of Mathematics Sigma, 3(2015), e13
  • [17] X Liang, RC Li, Extensions of Wielandt’s min–max principles for positive semi-definite pencils, Linear and Multilinear Algebra, 62(8), 1032-1048 (2014)
  • [18] Xin Liang and Ren-Cang Li, Trace minimization principles for positive semi-definite pencils, LINEAR ALGEBRA AND ITS APPLICATIONS, 438(2013), 7, 3085-3106

 

Update Time: 2025-10-13 17:00:06