BIMSA > 梁鑫
副研究员 梁鑫

团队: 偏微分方程理论与计算

办公室: A12-103

邮箱: liangxin@bimsa.cn

研究方向: 数值代数

个人简介

梁鑫，2009年获北京大学数学科学学院学士学位，2014年获该校博士学位。先后在德国马克斯普朗克复杂技术系统动力学研究所、新竹交通大学应用数学系从事博士后研究，曾在清华大学丘成桐数学科学中心任助理教授，2024年加入BIMSA任副研究员。从事数值代数和矩阵分析方向的研究，在特征值问题、代数Riccati方程等领域取得成果。主编《线性代数入门》教材。

研究兴趣

  • 数值线性代数
  • 矩阵分析
  • 代数特征值问题
  • 矩阵方程
  • 随机化算法

教育经历

  • 2011 - 2013      得克萨斯大学阿灵顿分校      计算数学      国家公派联合培养      (Supervisor: 李仁仓教授)
  • 2009 - 2014      北京大学      计算数学      理学博士      (Supervisor: 徐树方教授)
  • 2005 - 2009      北京大学      信息与计算科学      理学学士

工作经历

  • 2024 -      北京雁栖湖应用数学研究院      副研究员
  • 2021 - 2024      北京雁栖湖应用数学研究院      兼职助理研究员
  • 2018 - 2024      清华大学      助理教授
  • 2018 - 2018      得克萨斯大学阿灵顿分校      短期访问学者
  • 2016 - 2017      新竹交通大学      博士后
  • 2014 - 2016      马克斯普朗克复杂技术系统动力学研究所      博士后

荣誉与奖项

  • 2024      若琳奖
  • 2022      若琳奖

学术服务

  • -      International Journal for Numerical Methods in Engineering, Automatica, SIAM Journal on Matrix Analysis and Applications, Numerical Linear Algebra with Applications, Journal of Scientific Computing, Advances in Computational Mathematics, Linear Algebra and its Applications, Linear and Multilinear Algebra, International Journal of Robust and Nonlinear Control, Heliyon, Operators and Matrices, Special Matrices, Electronic Transactions on Numerical Analysis, Electronic Journal of Linear Algebra, Numerical Algebra Control and Optimization, Science China Mathematics, CSIAM Transactions on Applied Mathematics, Journal of Computational Mathematics, Mathematica Numerica Sinica, Journal of Numerical Methods and Computer Applications, Journal of Industrial and Management Optimization, Beijing Journal of Pure and Applied Mathematics, Mathematical Review      审稿人

出版物

  • [1] Zhechen Shen, and Xin Liang, Global Convergence Rate of Extended Steepest Descent Method for Computing Extreme Eigenvalues of Hermitian Matrices (2026)
  • [2] Huaming Ling, Chenglong Bao, Xin Liang, and Zuoqiang Shi, Semi-Supervised Clustering via Dynamic Graph Structure Learning, accepted by Beijing Journal of Pure and Applied Mathematics (2025)
  • [3] Zhen-Chen Guo, and Xin Liang, Flexible fixed-point iteration and its applications for nonsymmetric algebraic Riccati equations, arXiv: 2509.25942, submitted, in revision (2025)
  • [4] Zhechen Shen, and Xin Liang, Local convergence behavior of extended LOBPCG for computing eigenvalues of Hermitian matrices, arXiv: 2505.08218v4, submitted, in revision (2025)
  • [5] Xin Liang, and Ren-Cang Li, On Generalizing Trace Minimization Principles, II, LINEAR ALGEBRA AND ITS APPLICATIONS, 687, 8-37 (2024)
  • [6] Zhen-Chen Guo, and Xin Liang, An RADI-type method for stochastic continuous-time algebraic Riccati equations, arXiv:2403.02940, submitted (2024)
  • [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(4), 1749-1770 (2023)
  • [8] Xin Liang, On the optimality of the Oja’s algorithm for online PCA, Statistics and Computing, 33(3), 62 (2023)
  • [9] Zhen-Chen Guo and Xin Liang, The intrinsic Toeplitz structure and its applications in algebraic Riccati equations, NUMERICAL ALGORITHMS, 93(2023), 227-267
  • [10] 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
  • [11] 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
  • [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(6), e2445 (2022)
  • [13] Xin Liang, Zhen-Chen Guo, Tsung-Ming Huang, Tiexiang Li, and Wen-Wei 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)
  • [14] 梁鑫，田垠，杨一龙, 线性代数入门(2022)
  • [15] 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, 812-839 (2022)
  • [16] Xin Liang, Note on finding an optimal deflation for quadratic matrix polynomials, CSIAM Transactions on Applied Mathematics, 2(2), 336-356 (2021)
  • [17] 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
  • [18] Xin Liang and Ren-Cang Li, The hyperbolic quadratic eigenvalue problem, Forum of Mathematics Sigma, 3, e13 (2015)
  • [19] Xin Liang, and Ren-Cang Li, Extensions of Wielandt’s min–max principles for positive semi-definite pencils, Linear and Multilinear Algebra, 62(8), 1032-1048 (2014)
  • [20] Xin Liang and Ren-Cang Li, Trace minimization principles for positive semi-definite pencils, LINEAR ALGEBRA AND ITS APPLICATIONS, 438(7), 3085-3106 (2013)

 

更新时间: 2026-03-13 18:00:07