Personal Profile

         Weiwei Xu is a professor and doctoral supervisor at Nanjing University of Information Science and Technology, and an adjunct professor at Xi'an Jiaotong University. Her main research areas are matrix computation theory and its applications, and fundamental algorithms for big data analysis. She received her bachelor's degree from the School of Mathematical Sciences, South China Normal University in 2005 and her doctoral degree from the same institution in 2010. From September 2010 to June 2012, she conducted postdoctoral research at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences; from August 2014 to February 2015, she was a visiting scholar at theDepartment of Mathematics, National University of Singapore; from August 2019 to August 2020, she was a visiting scholar at the Department of Mathematics, University of Hong Kong; and from May 2022 to July 2023, she was a visiting scholar at the National Tianyuan Mathematics Northwest Center. 

          Representative research work includes establishing an optimization model for matrix trace functions representing generalized singular values and singular vectors with collaborators, providing a new idea and approach for solving generalized singular value and singular vector problems; and proposing a geometrically inexact Newton conjugate gradient method on Riemannian manifolds, for which global and quadratic convergence properties were established for the first time.

Together with collaborators, we have developed a new tool for matrix low-rank decomposition with online correction capabilities and a new theory of matrix stochastic renormalization.  Based on these advancements, we proposed a mathematical principle of "modeling energy concentration phenomena with approximately low-rank matrices and simplifying matrix computations through stochastic renormalization," and constructed a stochastic low-rank approximation method that adaptively identifies the optimal rank under accuracy constraints.  Furthermore, we developed the "XJTU-Pengcheng algorithm," which covers various matrix computation tasks. This algorithm reduces the computational cost of processing chips in base stations, significantly impacting the signal processing speed and overall performance of wireless communication systems using multi-antenna technology. This algorithm has already been applied by leading domestic companies.  In collaboration with colleagues, we utilized a new tool of low-rank matrix decomposition to propose a mixed-precision method for accurate SVD of low-rank matrices and optimized the GPU architecture, significantly improving computational performance.  The related theories and algorithms have been applied by leading companies. As the first author/corresponding author, I have published over 40 academic papers in prestigious international journals such as National Science Review, Math. Comput., SIAM J. Optim., SIAM J. Matrix Anal. Appl., SIAM Journal on Imaging Sciences, Advances in Space Research, and IEEE Transactions on Neural Networks and Learning Systems, as well as at the CCF A-class conference PPoPP 2026; completed one invention patent; led National Natural Science Foundation of China (NSFC) General Program and Youth Program projects, and provincial/ministerial level projects; and participated in a national key research and development program project of the Ministry of Science and Technology.

 Teaching curriculum

Linear algebra, matrix computation, computational methods, numerical linear algebra, numerical analysis, mathematical modeling, etc.

Representative publications

1 L. Shi¹,W.W. Xu^1*, S.S. Zhang^*,Towards Singular Value Decomposition for Rank-Deficient Matrices: An Efficient and Accurate Algorithm on GPU Architectures, PPoPP 2026，accepted, 2026.(Currently, some matrix algorithms are not specifically optimized for the low-rank characteristics of matrices, resulting in low overall computational performance. For example, NVIDIA's official cuSOLVER library only achieves 0.5 TFLOPs on the H100-PCIe GPU, while the GPU's peak performance is 51 TFLOPs. This means that computing low-rank SVD only utilizes less than 1% of the hardware's computational capabilities. This paper proposes a method utilizing partial replacement of Gram-Schmidt orthogonalization with Householder transformations and a mixed-precision approach, based on the matrix low-rank decomposition algorithm—the QB algorithm.  To address the time-consuming panel decomposition part of the Householder transformation, the TSQR method with reconstructed WY representation is used, improving the parallelism of the panel decomposition and reducing synchronization overhead on the GPU shared memory.  The proposed SVD algorithm is compared with the NVIDIA official library cuSOLVER SVD, achieving an acceleration of approximately 10 to 6700 times compared to the NVIDIA official library cuSOLVER.)

2 W.W. Xu, W.J. Shen, C. Liu, and Z.G. Jia^*,  A Novel Adaptive Low-Rank Matrix Approximation Method for Image Compression and Reconstruction, SIAM Journal on Imaging Sciences, 18 (2025), pp. 2127-2158. (We proposed an efficient orthogonal  decomposition method with automatic basis extraction, and a random low-rank approximation method with adaptive identification of the optimal rank, and developed a software package, see https://github.com/xuweiwei1/EOD-ABE.git)

3 Y.J. Wang, W.W. Xu^* and L. Zhu, Efficient Linear Discriminant Analysis based on Randomized Low-Rank Approaches, IEEE Transactions on Neural Networks and Learning Systems, 36 (2025), pp. 10028-10042. (To address the challenges of LDA in small sample problems and high computational costs, a new matrix low-rank approximation method was proposed, and a linear discriminant analysis software package was developed for dimensionality reduction and classification of data such as images, genes, and mass spectrometry data., code: https://github.com/xuweiwei1/fgsvd_lda.git)

4 T.T.  Sun, X.F. Peng, W.X. Ge^*, W.W. Xu, An improved preconditioned unsupervised K-means clustering algorithm, Computational Statistics, , 40 (2025), pp.4187-4207. https://doi.org/10.1007/s00180-025-01616-3.

5 W.W. Xu; Z.J. Bai^*; Double-variable Trace Maximization for Extreme Generalized Singular Quartets of A Matrix Pair: A Geometric Method, Mathematics of Computation, 349(2024), 2331-2359.

6 C. Xu; W.W. Xu^*; K.L. Jing; Fast Algorithms for Singular Value Decomposition and Inverse of Nearly Low-rank Matrices, National Science Review, vol. 10, 2023, DOI:10.1093/nsr/nwad083. （We propose an energy concentration modeling method based on approximate low-rank matrices, a matrix stochastic renormalization theory, and a mathematical principle for simplifying matrix calculations using stochastic renormalization.）

7 W.W. Xu; Y.M. Zhu; L. Zhu; J.Y. Lu^*; G.C. Wei; M. Wang; Y.X. Peng; A Class of Bayesian Machine Learning Model for Forecasting Dst During Intense Geomagnetic Storms, Advances in Space Research, 2023, 72: 3882-3889.

8 W.W. Xu^*; Michael K. Ng; A New Matrix Maximization Model for Computing Ratios of Generalized Singular Values from High-Order GSVD, Journal of Scientific Computing, 2023, 94: 35-57.

9 W.W. Xu; Michael K. Ng; Z.J. Bai^*; Geometric Inexact Newton Method for Generalized Singular Values of Grassmann Matrix Pair, SIAM Journal on Matrix Analysis and Applications, 2022, 43: 535-560.

10 W.W. Xu; W. Li^* ; L. Zhu; X.P. Huang; The Analytic Solutions of a Class of Constrained Matrix Minimization and Maximization Problems with Applications, SIAM Journal on Optimization, 2019, 29(2): 1657-1686.

11 W.W. Xu^*; L.J. Ma, L. Zhu and H. Liu; On Interval Estimates of Perturbations of Generalized Eigenvalues for Diagonalizable Pairs, Linear Algebra and its Applications, 2019, 562: 15-43.

12 W.W. Xu; H.K. Pang; W. Li^*; X.P. Huang; W.J. Guo; On the Explicit Expression of Chordal Metric Between Generalized Singular Values of Grassman Matrix Pairs with Applications, SIAM Journal on Matrix Analysis and Applications, 2018, 39(4): 1547-1563.

13 W.W. Xu; Modified General Modulus-based Matrix Splitting Method for Linear Complementarity Problems of H-matrices, Numerical Linear Algebra with Applications, 2015, 12(5): 748-760.

(* Corresponding author; 1 Co-first author)

Others

Outstanding Core Teachers of the Jiangsu Provincial Qinglan Project in 2019;

In 2022, she was awarded the Tianyuan Scholar title by the National Tianyuan Mathematics Northwest Center;

In 2022, he led the Xi'an Jiaotong University-Huawei Joint Laboratory team in participating in the Guangdong-Hong Kong-Macao Greater Bay Area (Huangpu) International Algorithm and Computing Competition, winning first place;

Media coverage: People's Daily, China Science and Technology Network, etc.

https://wap.peopleapp.com/article/7042673/6897201

http://m.stdaily.com/index/kejixinwen/202212/9b019b8c25c249128bd042eae3a27c80.shtml

Academic positions

Member of the Big Data and Artificial Intelligence Committee of the China Society for Industrial and Applied Mathematics;

Young Board Member of the Mathematical and Intelligent Systems Branch of the Operations Research Society of China