曾超

2006.9 - 2010.7 中国科学技术大学，本科

2011.9 - 2016.6 中国科学技术大学，博士

2022.2 - 南开大学数学科学学院，副教授

2021.7 - 2021.8 南开大学数学科学学院，访问学者

2019.9 - 2020.9 香港大学数学系，博士后

2018.9 - 2019.9 香港浸会大学数学系，博士后

2016.7 - 2018.6 南开大学数学科学学院，博士后

曾超，南开大学数学科学学院副教授。分别于 2010 年和 2016 年在中国科学技术大学大学获得学士和博士学位。曾在南开大学、香港浸会大学、香港大学从事博士后研究工作。2022 年加入南开大学数学科学学院。研究领域为数值代数、数值优化、数值逼近与计算几何。近年来在计算数学知名杂志比如 Numerische Mathematik，SIAM Journal on Numerical Analysis，SIAM Journal on Matrix Analysis and Applications，SIAM Journal on Imaging Sciences 等上发表多篇学术论文。

张量分析与计算

张量是表示多重线性函数与多维数组的有力工具，二阶张量就是我们熟知的矩阵。张量在多项式计算、信号（图像、视频）处理中，都扮演着重要角色。代表性论文：

Chao Zeng, Michael K. Ng, Incremental CP tensor decomposition by alternating minimization method, SIAM Journal on Matrix Analysis and Applications, 2021

Chao Zeng, Tai-Xiang Jiang, Michael K. Ng, An approximation method of CP rank for third-order tensor completion, Numerische Mathematik, 2021

不适定问题（图像处理、矩阵计算、张量计算等等）的计算方法

适定问题是指解满足下面三个要求的问题：解是存在的；解是唯一的；解是稳定的。这三个要求中，只要有一个不满足，则称之为不适定问题。在图像处理、矩阵（张量）计算等领域中，不适定问题非常常见。比如图像去噪是经典的不适定问题。代表性论文：

Chao Zeng, Chunlin Wu, On the edge recovery property of noncovex nonsmooth regularization in image restoration, SIAM Journal on Numerical Analysis, 2018

Chao Zeng, Rui Jia, Chunlin Wu, An iterative support shrinking algorithm for non-Lipschitz optimization in image restoration, Journal of Mathematical Imaging and Vision, 2019

多元样条与计算机辅助几何设计（Computer Aided Geometric Design）

多元样条是满足一定光滑性要求的分片多项式，它是表示函数与几何的有力工具。代表性论文：

Chao Zeng, Meng Wu, Fang Deng, Jiansong Deng, Dimensions of spline spaces over non-rectangular T-meshes, Advances in Computational Mathematics, 2016

Chao Zeng, Fang Deng, Jiansong Deng, Bicubic hierarchical B-Splines: Dimensions, completeness, and bases, Computer Aided Geometric Design, 2015

MathSciNet Index

21. Yuan Liu, Chunlin Wu, Chao Zeng,  Non-Lipschitz variational models and their iteratively reweighted least squares algorithms for image denoising on surfaces, SIAM Journal on Imaging Sciences,  17 (2024), 1255-1283.

20. Chao Zeng, On the tensor spectral p-norm and its higher order power method,  Calcolo, 61, 38, (2024).

19. Chao Zeng, Michael K. Ng, Tai-Xiang Jiang,  Incremental algorithms for truncated higher-order singular value decompositions,  BIT Numerical Mathematics, 64, 4, (2024).

18. Chao Zeng, Further results on tensor nuclear norms, Calcolo, 60, 34, (2023). 

17. Chao Zeng, Proximal linearization methods for Schatten p-quasi-norm minimization, Numerische Mathematik, 153(1), 213-248 (2023). 

16. Chao Zeng, Rank properties and computational methods for orthogonal tensor decompositions, Journal of Scientific Computing, 94, 6 (2023). 

15. Chao Zeng, Michael K. Ng, Incremental CP tensor decomposition by alternating minimization method, SIAM Journal on Matrix Analysis and Applications, 42 (2021) 832-858. 

14. Chao Zeng, Tai-Xiang Jiang, Michael K. Ng, An approximation method of CP rank for third-order tensor completion, Numerische Mathematik, 147 (2021), 727-757. 

13. Zhuoheng He, Michael K. Ng, Chao Zeng, Generalized singular value decompositions for tensors and their applications, Numerical Mathematics: Theory, Methods and Applications, 14 (2021), 692-713.

12. Chao Zeng, Michael K. Ng, Decompositions of third-order tensors: HOSVD, T-SVD, and beyond, Numerical Linear Algebra with Applications, 27 (2020), e2290. 

11. Chao Zeng, Chunlin Wu, On the discontinuity of images recovered by noncovex nonsmooth regularized isotropic models with box constraints, Advances in Computational Mathematics, 45 (2019), 589-610.

10. Chao Zeng, Chunlin Wu, Rui Jia, Non-Lipschitz models for image restoration with impulse noise removal, SIAM Journal on Imaging Sciences, 12 (2019), 420-458. 

9. Chao Zeng, Rui Jia, Chunlin Wu, An iterative support shrinking algorithm for non-Lipschitz optimization in image restoration, Journal of Mathematical Imaging and Vision, 61 (2019), 122-139. 

8. Xue Feng, Chunlin Wu, Chao Zeng, On the local and global minimizers of ℓ 0 gradient regularized model with box constraints for image restoration, Inverse Problems, 34 (2018), 095007. 

7. Chao Zeng, Chunlin Wu, On the edge recovery property of noncovex nonsmooth regularization in image restoration, SIAM Journal on Numerical Analysis, 56 (2018), 1168-1182. 

6. Chao Zeng, Jiansong Deng, On the dimension of trivariate spline spaces with the highest order smoothness on 3D T-meshes, Advances in Computational Mathematics, 44 (2018), 423-451. 

5. Fang Deng, Chao Zeng, Meng Wu, Jiansong Deng, Bases of biquadratic polynomial spline spaces over hierarchical T-meshes, Journal of Computational Mathematics, 35 (2017), 91-120. 

4. Chao Zeng, Meng Wu, Fang Deng, Jiansong Deng, Dimensions of spline spaces over non-rectangular T-meshes, Advances in Computational Mathematics, 42 (2016), 1259-1286. 

3. Fang Deng, Chao Zeng, Jiansong Deng, Boundary-mapping parametrization in isogeometric analysis, Communications in Mathematics and Statistics, 4 (2016), 203-216. 

2. Chao Zeng, Fang Deng, Jiansong Deng, Bicubic hierarchical B-Splines: Dimensions, completeness, and bases, Computer Aided Geometric Design, 38 (2015), 1-23.

1. Chao Zeng, Fang Deng, Xin Li, Jiansong Deng, Dimensions of biquadratic and bicubic spline spaces over hierarchical T-meshes, Journal of Computational and Applied Mathematics, 287 (2015), 162-178.