许进超 Jinchao Xu

人才培养

代表性论文 全部论文 毕业论文

• Parallel multilevel preconditioners, Mathematics of Computation 55(191) 1–22, 1990. J. Bramble, J. Pasciak, J. Xu. 被引 1125
  Comments: Known as Bramble-Pasciak-Xu Preconditioner: one of the two most basic and most widely used multilevel algorithms for numerical solution of partial differential equations.
• Convergence estimates for Multigrid algorithms without regularity assumptions, Mathematics of Computation 57(195) 23–45, 1991. J. Bramble, J. Pasciak, J. Wang, J. Xu. 被引 407
  Comments: A very impactful theory on a general framework that unifies the design and the analysis of a large number of iterative methods in scientific computing.
• Iterative methods by space decomposition and subspace correction, SIAM Review 34(4) 581–613, 1992. J. Xu. 被引 1681
  Comments: A ground-breaking theory that made it possible for convergence anlysis of multigrid methods for pratical problems.
• The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids, Computing 56(3) 215–235, 1996. J. Xu. 被引 273
  Comments: The first multigrid algorithm with rigorous optimal convergence theory for general unstructured grids.
• Two-grid discretization techniques for linear and nonlinear PDEs, SIAM Journal on Numerical Analysis 33(5) 1759–1777, 1996. J. Xu. 被引 847
  Comments: A general multiscale algorithm design framework and theory for a large class of linear and nonlinear partial differenial equations; it triggered a great number of follow-up works including numerous PhD theses from different fields.
• The method of alternating projections and the method of subspace corrections in Hilbert space, Journal of the American Mathematical Society 15(3) 573–597, 2002. J. Xu, L. Zikatanov. 被引 321
  Comments: The main result is now known as Xu-Zikatanov (XZ) identity. It provides a sharp convergence theory for both the method of subspace corrections (MSC) and the method of alternating projections (MAP). The first sharp convgence theory of MAP was first developed by von Neumann in 1930 for two subspaces case and the XZ identity solved a long-time open problem for sharp convergence analysis for multiple subspace case. It is among the earlist computational math paper published in 顶级纯数学期刊.
• Nodal auxiliary space preconditioning in H(curl) and H(div) spaces, SIAM Journal on Numerical Analysis 45(6) 2483–2509, 2007. R. Hiptmair, J. Xu. 被引 453
  Comments: HX 预条件子2008年被美国能源部列为计算科学领域的十大突破之一（链接），并呈送美国国会.
• Algebraic Multigrid methods, Acta Numerica, 26, 591–721, 2017. J. Xu, L. Zikatanov. 被引 307
  Comments: In this invited paper, a unified framework and theory is developed to derive and analyze in a coherent manner for a large variety of algebraic multigrid (AMG) methods for solving large-scale systems of equations.
• MgNet: a unified framework of Multigrid and convolutional neural network, Science China Mathematics, 62, 1331–1354, 2019. J. He, J. Xu. 被引 168
  Comments: This paper relates two totally different fields, namely multigrid methods for solving partial differential equations and convolutional neural networks for image classification, by a unified algorithm known as MgNet. In particular, it shows that an effective and new class of convolutional neural network models can be directly obtained by making some minor modifications to a geometric multigrid method.
• ReLU deep neural networks and linear finite elements, Journal of Computational Mathematics, 38(3), 502–527, 2020. J. He, L. Li, J. Xu, C. Zheng. 被引 436
  Comments: This paper provides a rigorous and insightful comparison between ReLU deep neural networks and linear finite elements, shedding light on their approximation capabilities and structural analogies.
• Characterization of the variation spaces corresponding to shallow neural networks, Constructive Approximation, 57(3), 1109–1132, 2023. J. Siegel, J. Xu. 被引 47
  Comments: By characterizing the variation spaces of shallow networks, this work deepens our understanding of the expressivity and inherent limitations of neural architectures under norm constraints.
• Sharp bounds on the approximation rates, metric entropy, and n-widths of shallow neural networks, Foundations of Computational Mathematics, 24, 481–537, 2024. J. Siegel, J. Xu. 被引 95
  Comments: This work establishes sharp bounds on the approximation rates, metric entropy, and $n$-widths of shallow neural networks, offering a comprehensive and quantitatively precise analysis of their complexity and expressive power.
• Second Language (Arabic) Acquisition of LLMs via Progressive Vocabulary Expansion, ACL2025. J. Zhu, H. Huang, Z. Lin, J. Liang, Z. Tang, K. Almubarak, A. Alharthik, B. An, J. He, X. Wu, F. Yu, J. Chen, Z. Ma, Y. Du, H. Zhang, E. A. Alghamdi, L. Zhang, R. Sun, H. Li, B. Wang, J. Xu
  Comments: 入选ACL2025 oral presentation (入选率不足10%) 和 panel discussion (入选率不足1%).