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勘误表 10--11章草稿（高等线性代数选讲部分讲义） 教学录像 出版社书页

个人时间线

研究兴趣

数值线性代数、矩阵计算、矩阵分析

学术作品

教材

[B1] 梁鑫*, 田垠, 杨一龙. 《线性代数入门》, 清华大学出版社，北京，2022.06. ISBN: 978-7-302-60971-1.

预印本

[P2] Z.-C. Guo and X. Liang*. Flexible fixed-point iteration and its applications for nonsymmetric algebraic Riccati equations, 2025. arXiv: 2509.25942 [math.NA]. 21 pages.

[P1] Z.-C. Guo and X. Liang*. An RADI-type method for stochastic continuous-time algebraic Riccati equations, 2024. arXiv: 2403.02940v2 [math.NA]. 21 pages.

期刊论文

[J16] Z. Shen and X. Liang*. Local convergence behavior of extended local optimal block preconditioned conjugate gradient method for computing eigenvalues of {Hermitian} matrices. Numer. Lin. Alg. Appl., 33:e70075, 2026. 24 pages. link arXiv: 2505.08218

[J15] H. Ling, C. Bao, X. Liang, and Z. Shi*. Semi-supervised clustering via dynamic graph structure learning, Beijing J. Pure Appl. Math., 3(1):181–216, 2026. link arXiv: 2209.02513

[J14] X. Liang* and R.-C. Li. On generalizing trace minimization principles, II. Linear Algebra Appl., 687:8–37, 2024. link arXiv: 2303.13092

[J13] Z.-C. Guo and X. Liang*. Stochastic algebraic Riccati equations are almost as easy as deterministic ones theoretically. SIAM J. Matrix Anal. Appl., 44(4):1749–1770, 2023. link arXiv: 2207.11220

[J12] X. Liang, Z.-C. Guo, L. Wang, R.-C. Li*, and W.-W. Lin. Nearly optimal stochastic approximation for online principal subspace estimation. Sci. China Math., 66:1087–1122, 2023. link arXiv: 1711.06644

[J11] Z.-C. Guo and X. Liang*. The intrinsic Toeplitz structure and its applications in algebraic Riccati equations. Numer. Alg., 93:227–267, 2023. link arXiv: 2111.13003

[J10] X. Liang*. On the optimality of the Oja's algorithm for online PCA. Stat. Comput., 33:e62, 2023. 11 pages. link arXiv: 2104.00512

[J9] X. Liang, L. Wang, L.-H. Zhang, and R.-C. Li*. On generalizing trace minimization principles. Linear Algebra Appl., 656:483–509, 2023. link arXiv: 2104.00257

[J8] X. Jia, X. Liang, C. Shen, and L.-H. Zhang*. Solving the cubic regularization model by a nested restarting Lanczos method. SIAM J. Matrix Anal. Appl., 43(2):812–839, 2022. link

[J7] P. Benner and X. Liang*. Convergence analysis of vector extended locally optimal block preconditioned extended conjugate gradient method for computing extreme eigenvalues. Numer. Lin. Alg. Appl., 29:e2445, 2022. 24 pages. link arXiv: 2004.14002

[J6] X. Liang*, Z.-C. Guo, T.-M. Huang, T. Li, and W.-W. Lin. Bifurcation analysis of the eigenstructure of discrete single-curl operator in three-dimensional Maxwell's equations with Pasteur media. IMA J. Numer. Anal., 42(4):3735–3770, 2022. link arXiv: 2012.00479

[J5] X. Liang*. Note on finding an optimal deflation for quadratic matrix polynomials. CSIAM Trans. Appl. Math., 2(2):336–356, 2021. link

[J4] P. Benner, X. Liang, S. Miodragović*, and N. Truhar. Relative perturbation theory for quadratic Hermitian eigenvalue problems. Linear Algebra Appl., 618:97–128, 2021. link arXiv: 1602.03420

[J3] X. Liang and R.-C. Li*. The hyperbolic quadratic eigenvalue problem. Forum of Mathematics, Sigma, 3:e13, 2015. 93 pages. link

[J2] X. Liang and R.-C. Li*. Extensions of Wielandt’s min-max principles for positive semi-definite pencils. Linear Multilinear Algebra, 62(8):1032–1048, 2014. link

[J1] X. Liang, R.-C. Li*, and Z. Bai. Trace minimization principles for positive semi-definite pencils. Linear Algebra Appl., 438(7):3085–3106, 2013. link

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