Lexing Ying

Lexing Ying (Lex)

Professor of Mathematics
Stanford University

Phone: 650-723-2221

Email: lexing at stanford dot edu

Address:
Department of Mathematics
450 Jane Stanford Way, Bldg 380
Stanford University
Stanford, CA 94305-2125

Office hour in Winter 2024: TTh 12-1pm

Various committees handle hiring and admission processes. I'm unable to address the majority of emails related to these matters.

Recent research talks

Eigenmatrix for unstructured sparse recovery [Link]
Multimodal Sampling via Approximate Symmetries [Link] (17:00-36:00)
Quantum pseudo-differential operators and Robust QPE [Link]
Quantum numerical analysis [Link]
Some Mathematical Aspects of Deep Learning and Stochastic Gradient Descent [Link]
Correcting convexity bias [Link]
Prony's method, analytic continuation, and quantum signal processing [Link]
Optimization formulations and algorithms of Markov decision problems [Link]
Neural networks and partial differential equations [Link]
Sobolev Regularization Effect of SGD for NNs [Link]
Solving inverse problems with deep learning [Link]

Technology impacts

Co-developed the directional fast multipole method for high frequency wave equation kernels.
See [PDF] for the original paper.
Co-developed the Pole EXpansion and Selected Inversion (PEXSI) method for electronic structure calculation [Link]. PESXI has been adopted in BigDFT, CP2K, FHI-aims, SIESTA, etc.
Co-developed the Selected Columns of Density Matrix (SCDM) method for computing Wannier functions. SCDM has been integrated into Wannier90.
See [PDF] for the original paper.
Co-developed the Interpolative Separable Density Fitting (ISDF) method for compressing high order tensors derived from orbitals.
See [PDF] for the original paper.
Co-developed the pivoted-QR spectral clustering algorithm. It is in the main branch of the python scikit-learn library as one of three default algorithms for cluster assigning in a spectral embedding.
See [PDF] for the original paper.

Teaching

The webpages of my current courses are hosted at canvas.stanford.edu
Winter 2024: MATH 220B/CME 306, Computational Methods of Applied Mathematics.
Winter 2024: MATH 275B, Physical Models of Applied Mathematics (topics in applied mathematics).

Students and postdocs
Current

Haoxuan Chen
Alice Cortinovis (postdoc co-advised with Emmanuel Candes)
Ya-Chi Chu (co-advised with Madeleine Udell)
Rajat Dwaraknath (co-advised with Mert Pilanci)
Milo Marsden (co-advised with Persi Diaconis)
Hongkang Ni
Leah Reeder
Yinuo Ren (co-advised with Grant Rotskoff)
Xun Tang

----PhD students
Haoya Li (2024)
Yiping Lu (2023, co-advised with Jose Blanchet)
Zach Izzo (2023, co-advised with James Zou)
Philip Etter (2022)
Panagiotis Lolas (2022, co-advised with Iain Johnstone)
Cindy Catherine Orozco Bohorquez (2021)
Jordi Feliu Faba (2021)
Jing An (2021)
Fei Liu (2018)
Victor Minden (2017)
Yingzhou Li (2017)
Anil Damle (2016)
Haizhao Yang (2015)
Paul Tsuji (2012)
Jack Poulson (2012)
Phillip Schmitz (2010)
----Postdocs
Chao Ma (2023)
Yuhua Zhu (2022)
Yuwei Fan (2019)
Yuehaw Khoo (2019)
Kenneth Ho (2015)
Jingwei Hu (2014)

Awards

SIAM Fellow, 2024.
Invited lecture, The International Congress of Mathematicians, 2022.
ICCM Morningside Silver Medal of Applied Mathematics, 2016.
SIAM James H. Wilkinson Prize in Numerical Analysis and Scientific Computing, 2013.
Feng Kang Prize of Scientific Computing, 2011.
National Science Foundation CAREER Award, 2009.
Alfred P. Sloan Research Fellowship, 2007.

Publications
Preprints

Lexing Ying. A note on continuous-time online learning [Link]
Hongkang Ni, Lexing Ying. Quantum wave packet transforms with compact frequency support. [Link]
Lexing Ying. A perturbative analysis for noisy spectral estimation. [Link]
Xun Tang, Leah Collis, Lexing Ying. Solving high-dimensional Kolmogorov backward equations with functional hierarchical tensor operator. [Link]
Xun Tang, Holakou Rahmanian, Michael Shavlovsky, Kiran Koshy Thekumparampil, Tesi Xiao, Lexing Ying. A Sinkhorn-type Algorithm for Constrained Optimal Transport. [Link]
Lexing Ying. Multidimensional unstructured sparse recovery via eigenmatrix. [Link]
Alice Cortinovis, Lexing Ying. A sublinear-time randomized algorithm for column and row subset selection based on strong rank-revealing QR factorizations. [Link]
Hongrui Chen, Lexing Ying. Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization. [Link]
Zhiyan Ding, Haoya Li, Lin Lin, Hongkang Ni, Lexing Ying, Ruizhe Zhang, Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method. [Link]
Haoxuan Chen, Lexing Ying. Ensemble-Based Annealed Importance Sampling. [Link]
Lexing Ying. Multimodal Sampling via Approximate Symmetries. [Link]
Haoya Li, Yu Tong, Hongkang Ni, Tuvia Gefen, Lexing Ying. Heisenberg-limited Hamiltonian learning for interacting bosons. [Link]
Alice Cortinovis, Lexing Ying. Computing Free Convolutions via Contour Integrals. [PDF]
Yiping Lu, Wenlong Ji, Zach Izzo, Lexing Ying. Importance Tempering: Group Robustness for Overparameterized Models. [PDF]
Chao Ma and Lexing Ying. Correcting Convexity Bias in Function and Functional Estimate. [PDF]
Panagiotis Lolas, Lexing Ying. Shrinkage Estimation of Functions of Large Noisy Symmetric Matrices. [PDF]
Cindy Orozco Bohorquez, Yuehaw Khoo, Lexing Ying. Maximizing robustness of point-set registration by leveraging non-convexity. [PDF]

Refereed Journal and Conference Papers

Xun Tang, Lexing Ying. Solving high-dimensional Fokker-Planck equation with functional hierarchical tensor. To appear in JCP. [Link]
Kaizhao Liu, Jose Blanchet, Lexing Ying, Yiping Lu. Orthogonal Bootstrap: Efficient Simulation of Input Uncertainty. ICML 2024. [Link]
Yiping Lu, Jiajin Li, Lexing Ying, Jose Blanchet. Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controls. 40th Conference on Uncertainty in Artificial Intelligence (UAI 2024) Oral presentation. [PDF]
Hongkang Ni, Haoya Li, Lexing Ying. Quantum Hamiltonian Learning for the Fermi-Hubbard Model. To appear in Acta Applicandae Mathematicae. [Link]
Lexing Ying. Eigenmatrix for unstructured sparse recovery. Applied and Computational Harmonic Analysis, 2024. [Link] [Code].
Xun Tang, Michael Shavlovsky, Holakou Rahmanian, Elisa Tardini, Kiran Koshy Thekumparampil, Tesi Xiao, Lexing Ying. Accelerating Sinkhorn algorithm with sparse Newton iterations. ICLR 2024. [Link]
Yinuo Ren, Chao Ma, Lexing Ying. Understanding the Generalization Benifits of Late Learning Rate Decay. AISTAT 2024. [Link]
Yinuo Ren, Yiping Lu, Lexing Ying, Grant M. Rotskoff. Statistical Spatially Inhomogeneous Diffusion Inference. AAAI 2024. [Link]
Yinuo Ren, Tesi Xiao, Tanmay Gangwani, Anshuka Rangi, Holakou Rahmanian, Lexing Ying, Subhajit Sanyal. Multi-Objective Optimization via Wasserstein-Fisher-Rao Gradient Flow. AISTAT 2024 [Link]
Haoya Li, Hsiangfu Yu, Lexing Ying, Inderjit Dhillon, Accelerating Primal-dual Methods for Regularized Markov Decision Processes. SIAM Journal on Optimization. [PDF]
Haoya Li, Hongkang Ni, Lexing Ying. Adaptive low-depth quantum algorithms for robust multiple-phase estimation. Physical Review A. [PDF]
Hongkang Ni, Haoya Li, Lexing Ying. On low-depth algorithms for quantum phase estimation. Quantum. [PDF]
Lin Lin, Jianfeng Lu, and Lexing Ying. Recent progresses for evaluating the Kohn-Sham map, Density Functional Theory: Modeling, Mathematical Analysis, Computational Methods, and Applications. ed. Eric Cances and Gero Friesecke, Springer 2023.
Rajat Dwaraknath, Lexing Ying. On Optimization Formulations of Finite Horizon MDPs, OPT NeurIPS 2023 Workshop.
Jose Blanchet, Haoxuan Chen, Yiping Lu, Lexing Ying. When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimality. NeurIPS 2023. [ARXIV]
Yuhua Zhu, Zach Izzo, Lexing Ying. Continuous-in-time Limit for Bayesian Bandits. Journal of Machine Learning Research. [PDF]
Philip A. Etter, Lexing Ying. Operator Shifting for Noisy Elliptic Systems. Research in the Mathematical Sciences. [PDF]
Chao Ma, Lexing Ying. Why self-attention is Natural for Sequence-to-Sequence Problems? A Perspective from Symmetries. Journal of Machine Learning. [PDF]
Haoya Li, Hongkang Ni, Lexing Ying. A note on spike localization for line spectrum estimation. Applied and Computational Harmonic Analysis, 2023. [PDF]
Yinuo Ren, Hongli Zhao, Yuehaw Khoo, Lexing Ying. High-dimensional density estimation with tensorizing flow. Research in the Mathematical Sciences. [PDF]
Haoya Li, Hongkang Ni, Lexing Ying. On efficient quantum block encoding of pseudo-differential operators. Quantum [PDF]
Haoya Li, Samarth Gupta, Hsiangfu Yu, Lexing Ying, Inderjit Dhillon. Approximate Newton policy gradient algorithms. SIAM Journal on Scientific Computing. [PDF]
Xun Tang, YoonHaeng Hur, Yuehaw Khoo, Lexing Ying. Generative Modeling via Tree Tensor Network States. Research in the Mathematical Sciences. [PDF]
Samarth Gupta, Daniel N. Hill, Lexing Ying, Inderjit Dhillon, Bayesian regularization of empirical MDPs. ICLR RRL workshop 2023.[PDF]
Xun Tang, Lexing Ying, and Yuhua Zhu, Operator Shifting for Model-based Policy Evaluation. Communications in Mathematical Sciences. [PDF]
Jikai Jin, Yiping Lu, Jose Blanchet, Lexing Ying. Minimax Optimal Kernel Operator Learning via Multilevel Training. ICLR 2023 (spotlight). [PDF]
Yuhua Zhu and Lexing Ying. Variational Actor-Critic Algorithms. ESAIM: Control, Optimisation and Calculus of Variations. [PDF]
Phillip Etter, Yuwei Fan, and Lexing Ying. Coarse-Proxy Reduced Basis Methods for Integral Equations. Journal of Computational Physics. [PDF]
Jing An, Lexing Ying. Combining resampling and reweighting for faithful stochastic optimization. Communications in Mathematical Sciences. [PDF]
Lexing Ying. Annealed importance sampling for Ising models with mixed boundary conditions. Journal of Computational Mathematics. [PDF]
Lexing Ying. Double Flip Move for Ising Models with Mixed Boundary Conditions. Journal of Computational Mathematics. [PDF]
Lexing Ying. Stable factorization for phase factors of quantum signal processing. Quantum. [PDF] [CODE]
Yifan Peng, Lin Lin, Lexing Ying, Leonardo Zepeda-Nunez. Efficient Long-Range Convolutions for Point Clouds. Journal of Computational Physics. [PDF]
Yuwei Fan and Lexing Ying. Solving Traveltime Tomography with Deep Learning. Communications in Mathematics and Statistics. [PDF]
Yiping Lu, Jose Blanchet, Lexing Ying. Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent. NeurIPS 2022. [PDF]
Philip A. Etter, Lexing Ying. Operator Shifting for General Noisy Matrix Systems. SIAM Journal on Mathematics of Data Science. [PDF]
Lexing Ying. Analytic continuation from limited noisy Matsubara data. Journal of Computational Physics. [PDF]
Lexing Ying. Pole recovery from noisy data on imaginary axis. Journal of Scientific Computing. [PDF]
Chao Ma and Lexing Ying. A Riemannian Mean Field Formulation for Two-layer NeuralNetworks with Batch Normalization. Research in the Mathematical Sciences. [PDF]
Chao Ma, Daniel Kunin, Lei Wu, Lexing Ying. Beyond the Quadratic Approximation: the Multiscale Structure of Neural Network Loss Landscapes. Journal of Machine Learning. [PDF]
J. Yao, H. Li, M. Bukov, L. Lin, L. Ying, Monte Carlo tree search based hybrid optimization of variational quantum circuits. MSML 2022. [PDF]
Yuwei Fan and Lexing Ying. Solving optical tomography with deep learning. Annals of Mathematical Sciences and Applications. [PDF]
Philip A. Etter, Kai Zhong, Hsiang-Fu Yu, Lexing Ying, Inderjit Dhillon. Enterprise-Scale Search: Accelerating Inference for Sparse Extreme Multi-Label Ranking Trees. WWW 2022.[PDF]
Lexing Ying. On Lyapunov functions and particle methods for regularized minimax problems. Research in the Mathematical Sciences. [PDF]
Yiping Lu, Haoxuan Chen, Jianfeng Lu, Lexing Ying, Jose Blanchet, Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality. ICLR 2022. [PDF]
Chao Ma and Lexing Ying. Provably convergent quasistatic dynamics for mean-field two-player zero-sum games. ICLR 2022. [PDF]
Zachary Izzo, Lexing Ying, and James Zou, How to Learn when Data Gradually Reacts to Your Model. AISTATS 2022. [PDF]
Yingzhou Li, Jack Poulson, Lexing Ying. Distributed-memory H-matrix Algebra 1: Data distribution and matrix-vector multiplication. CSIAM Trans. Appl. Math., 2 (2021), pp. 431-459. [PDF]
Haoya Li, Lexing Ying. A semigroup method for high dimensional elliptic PDEs and eigenvalue problems based on neural networks. JCP. [PDF]
Yuwei Fan and Lexing Ying. Solving Inverse Wave Scattering with Deep Learning. Annals of Mathematical Sciences and Applications. [PDF]
Lexing Ying. Solving Inverse Problems with Deep Learning. ICM 2022. [PDF]
Chao Ma, Lexing Ying. On Linear Stability of SGD and Input-Smoothness of Neural Networks. NeurIPS 2021[PDF]
Lexing Ying, Yuhua Zhu, A Note on Optimization Formulations of Markov Decision Processes. Communications in Mathematical Sciences. [PDF]
Jordi Feliu-Fabà, Lexing Ying. Approximate inversion of discrete Fourier integral operators. Journal of Computational Physics. [PDF]
Jordi Feliu-Faba, Lexing Ying. Hierarchical Interpolative Factorization Preconditioner for Parabolic Equations. Journal of Scientific Computing. [PDF]
Jing An and Lexing Ying. On the gradient flow structure of the isotropic Landau equation. Communications in Mathematical Sciences. [PDF]
Lukas Einkemmer, Jingwei Hu, Lexing Ying. An efficient dynamical low-rank algorithm for the Boltzmann-BGK equation close to the compressible viscous flow regime. SIAM Journal of Scientific Computing. [PDF]
Chao Ma, Lexing Ying. Achieving Adversarial Robustness Requires An Active Teacher. Journal of Computational Mathematics. [PDF]
Rajat Sen, Alexander Rakhlin, Lexing Ying, Rahul Kidambi, Dean Foster, Daniel Hill, Inderjit Dhillon. Top-k eXtreme Contextual Bandits with Arm Hierarchy. ICML(2021). [PDF]
Zachary Izzo, Lexing Ying, James Zou. How to Learn when Data Reacts to Your Model: Performative Gradient Descent. ICML(2021). [PDF]
Haoya Li, Yuwei Fan, Lexing Ying. A Simple Multiscale Method for Mean Field Games. Journal of Computational Physics. [PDF]
Lexing Ying. A heuristic independent particle approximation to determinantal point processes. Journal of Scientific Computing. [PDF]
Haoya Li, Yuehaw Khoo, Yinuo Ren, Lexing Ying. A semigroup method for high dimensional committor functions based on neural network, MSML(2021). [PDF]
Yuhua Zhu, Zach Izzo, and Lexing Ying. Borrowing From the Future: Addressing Double Sampling in Model-free Control. MSML(2021). [PDF]
Jing An, Lexing Ying, Yuhua Zhu. Why resampling outperforms reweighting for correcting sampling bias. ICLR 2021. [PDF]
Yuehaw Khoo, Jianfeng Lu, and Lexing Ying. Efficient construction of tensor ring representations from sampling. SIAM Journal of Multiscale Modeling and Simulation. [PDF]
Jun Qin and Lexing Ying. Hierarchical Low-rank Structure of Parameterized Distributions. Communications in Mathematical Sciences. [PDF]
Yuhua Zhu and Lexing Ying. A Sharp Convergence Rate for a Model Equation of the Asynchronous Stochastic Gradient Descent. Communications in Mathematical Sciences. [PDF]
Zhihan Li, Yuwei Fan, and Lexing Ying. Multilevel Fine-Tuning: Closing Generalization Gaps in Approximation of Solution Maps under a Limited Budget for Training Data. SIAM MMS. [PDF]
Lexing Ying. Natural Gradient for Combined Loss Using Wavelets. Journal of Scientific Computing. [PDF]
Xin Ye, Jianlin Xia, Lexing Ying. Analytical low-rank compression via proxy point selection. SIMAX. [PDF]
Yuehaw Khoo, Lin Lin, Michael Lindsey, Lexing Ying. Semidefinite relaxation of multi-marginal optimal transport for strictly correlated electrons in second quantization. SISC. [PDF]
Lexing Ying. Mirror Descent Algorithms for Minimizing Interacting Free Energy. Journal of Scientific Computing 51 (2020). [PDF].
Yiping Lu, Chao Ma, Yulong Lu, Jianfeng Lu, Lexing Ying. A Mean-field Analysis of Deep ResNet and Beyond: Towards Provable Optimization via Overparameterization from Depth. ICML (2020). [PDF] [PDF]
Yuhua Zhu and Lexing Ying. Borrowing From the Future: An Attempt to Address Double Sampling. Mathematical and Scientific Machine Learning Conference (2020). [PDF]
Jordi Feliu-Faba, Yuwei Fan, and Lexing Ying. Meta-learning pseudo-differential operators with deep neural networks. Journal of Computational Physics 408 (2020). [PDF]
Yuwei Fan and Lexing Ying. Solving electrical impedance tomography with deep learning. Journal of Computational Physics 404 (2020). [PDF]
Victor Minden and Lexing Ying. A simple solver for the fractional Laplacian in multiple dimensions. SIAM Journal on Scientific Computing 42-2 (2020). [PDF]
Yuehaw Khoo, Jianfeng Lu, and Lexing Ying. Solving PDE problems with uncertainty using neural-networks. European Journal of Applied Mathematics (2020). [PDF]
Jordi Feliu-Faba, Kenneth Ho, and Lexing Ying. Recursively preconditioned hierarchical interpolative factorization for elliptic partial differential equations. Communications in Mathematical Sciences 18-1 (2020). [PDF]
Wuchen Li, Lexing Ying. Hessian transport gradient flows. Research in the Mathematical Sciences 6 (2019). [PDF]
Yuehaw Khoo and Lexing Ying. SwitchNet: a neural network model for forward and inverse scattering problems. SIAM Journal on Scientific Computing 41-5 (2019). [PDF]
Yuehaw Khoo and Lexing Ying. Convex relaxation approaches for strictly correlated density functional theory. SIAM Journal on Scientific Computing 41-4, (2019). [PDF]
Yuwei Fan, Lin Lin, Lexing Ying, and Leonardo Zepeda-Nunez, A multiscale neural network based on hierarchical matrices. SIAM Journal of Multiscale Modeling and Simulation 17-4, (2019) [PDF]
Jing An, Jianfeng Lu, and Lexing Ying. Stochastic modified equations for the asynchronous stochastic gradient descent. Information and Inference (2019). [PDF]
Lin Lin, Jianfeng Lu, and Lexing Ying. Numerical methods for Kohn-Sham density functional theory, Acta Numer. 2019.
Yuwei Fan, Jordi Feliu-Faba, Lin Lin, Lexing Ying, and Leonardo Zepeda-Nunez. A multiscale neural network based on hierarchical nested bases. Research in the Mathematical Sciences, 2019, Vol. 6 [PDF]
Yuwei Fan, Cindy Orozco Bohorquez, and Lexing Ying. BCR-Net: a neural network based on the nonstandard wavelet form. Journal of Computational Physics, 2019, Vol. 384. [PDF]
Yuwei Fan, Jing An, and Lexing Ying. Fast algorithms for integral formulations of steady-state radiative transfer equation. Journal of Computational Physics, 2019, Vol. 380 [PDF]
Fei Liu and Lexing Ying. Sparsifying preconditioner for the time-harmonic Maxwell’s equations. Journal of Computational Physics 376, (2019). [PDF]
Anil Damle, Victor Minden, and Lexing Ying. Simple, direct and efficient multi-way spectral clustering. Information and Inference 8 (2019). [PDF]
Yuehaw Khoo, Jianfeng Lu, and Lexing Ying. Solving for high dimensional committor functions using artificial neural networks. Research in the Mathematical Sciences 6 (1), 2018 [PDF]
Zhenning Cai, Yuwei Fan, and Lexing Ying. An entropic Fourier method for the Boltzmann equation. SIAM J. Sci. Comput. 40(5) (2018). [PDF]
Fei Liu and Lexing Ying. Sparsify and sweep: an efficient preconditioner for the Lippmann-Schwinger equation. SIAM Journal on Scientific Computing 40-2 (2018). [PDF]
Yingzhou Li, Haizhao Yang, and Lexing Ying. Multidimensional butterfly factorization. Applied and Computational Harmonic Analysis 44-3 (2018). [PDF]
Anil Damle, Lin Lin, and Lexing Ying. Computing localized representations of the kohn-sham subspace via randomization and refinement. SIAM Journal on Scientific Computing 39-6 (2017). [PDF]
Victor Minden, Anil Damle, Kenneth Ho, and Lexing Ying. Fast spatial Gaussian process maximum likelihood estimation via skeletonization factorizations. SIAM Journal of Multiscale Modeling and Simulation 15-4 (2017). [PDF]
Lexing Ying. Tensor network skeletonization. SIAM Journal of Multiscale Modeling and Simulation 15-4 (2017). [PDF]
Yingzhou Li and Lexing Ying. Distributed-memory hierarchical interpolative factorization. Research in the Mathematical Sciences 4 (2017). [PDF]
Fei Liu and Lexing Ying. Localized sparsifying preconditioner for periodic indefinite systems. Communications in Mathematical Sciences 15-4 (2017). [PDF]
Victor Minden, Kenneth Ho, Anil Damle, and Lexing Ying. A recursive skeletonization factorization based on strong admissibility. SIAM Multiscale Modeling and Simulation 15-2 (2017). [PDF]
Lin Lin, Ze Xu, and Lexing Ying. Adaptively compressed polarizability operator for accelerating large scale ab initio phonon calculations. SIAM Multiscale Modeling and Simulation 15-1 (2017). [PDF]
Anil Damle, Lin Lin, and Lexing Ying. SCDM-k: Localized orbitals for solids via selected columns of the density matrix. Journal of Computational Physics 334 (2017). [PDF]
Jianfeng Lu and Lexing Ying. Fast algorithm for periodic density fitting for Bloch waves. Annals of Mathematical Sciences and Applications 1-2 (2016). [PDF]
Jianfeng Lu and Lexing Ying. Sparsifying preconditioner for soliton calculations. Journal of Computational Physics 315 (2016). [PDF]
Fei Liu and Lexing Ying. Additive sweeping preconditioner for the Helmholtz equation. SIAM Multiscale Modeling and Simulation 14-2 (2016). [PDF]
Fei Liu and Lexing Ying. Recursive sweeping preconditioner for the 3D Helmholtz equation. SIAM Journal on Scientific Computing 38-2 (2016). [PDF]
Victor Minden, Anil Damle, Kenneth Ho, and Lexing Ying. A technique for updating hierarchical factorizations of integral operators. SIAM Multiscale Modeling and Simulation 14-1 (2016). [PDF]
Junzhe Sun, Sergey Fomel, and Lexing Ying. Lowrank one-step wave extrapolation for reverse-time migration. Geophysics 81-1 (2016).
Kenneth Ho and Lexing Ying. Hierarchical interpolative factorization for elliptic operators: differential equations. Communications in Pure and Applied Mathematics 69-8 (2016). [PDF]
Kenneth Ho and Lexing Ying. Hierarchical interpolative factorization for elliptic operators: integral equations. Communications in Pure and Applied Mathematics 69-7 (2016). [PDF]
Haizhao Yang, Jianfeng Lu, and Lexing Ying. Crystal image analysis using 2D synchrosqueezed transforms. SIAM Multiscale Modeling and Simulation 13-4 (2015). [PDF]
Jianfeng Lu and Lexing Ying. Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost. Journal of Computational Physics 302-1 (2015). [PDF]
Lexing Ying. Directional preconditioner for 2D high frequency obstacle scattering. SIAM Multiscale Modeling and Simulation 13-3 (2015). [PDF]
Haizhao Yang, Jianfeng Lu, W. Brown, I. Daubechies, and Lexing Ying. Quantitative canvas weave analysis using 2D synchrosqueezed transforms. IEEE Signal Processing Magazine 55 (2015). [PDF]
Yingzhou Li, Haizhao Yang, Eileen Martin, Kenneth Ho, and Lexing Ying. Butterfly factorization. SIAM Multiscale Modeling and Simulation 13-2 (2015). [PDF]
Lexing Ying. Sparsifying preconditioner for the Lippmann-Schwinger equation. SIAM Multiscale Modeling and Simulation 13-2 (2015). [PDF]
Yingzhou Li, Haizhao Yang, and Lexing Ying. A multiscale butterfly algorithm for multidimensional Fourier integral operators. SIAM Multiscale Modeling and Simulation 13-2 (2015). [PDF]
Anil Damle, Lin Lin, and Lexing Ying. Compressed representation of Kohn-Sham orbitals via selected columns of the density matrix. J. Chem. Theory Comput. 11 (2015) [PDF]
Lexing Ying. Sparsifying preconditioner for pseudospectral approximations of indefinite systems on periodic structures. SIAM Multiscale Modeling and Simulation 13-2 (2015). [PDF]
Lexing Ying. Fast directional computation of high frequency boundary integrals via local FFTs. SIAM Multiscale Modeling and Simulation 13-1 (2015). [PDF]
Jingwei Hu and Lexing Ying. A fast algorithm for the energy space boson Boltzmann collision operator. Mathematics of Computation 84 (2015). [PDF]
Jingwei Hu, Sergey Fomel, and Lexing Ying. A fast algorithm for 3D azimuthally anisotropic velocity scan. Geophysical Prospecting 63 (2015). [PDF]
Anil Damle, Lin Lin, and Lexing Ying. Pole expansion for solving a type of parametrized linear systems in electronic structure calculations. SIAM Journal on Scientific Computing 36 (2014). [PDF]
Austin Benson, Jack Poulson, Khoa Tran, Bjorn Engquist, and Lexing Ying. A parallel directional fast multipole method. SIAM Journal on Scientific Computing 36 (2014). [PDF]
Haizhao Yang and Lexing Ying. Synchrosqueezed curvelet transform for two-dimensional mode decomposition. SIAM Journal on Mathematical Analysis 46 (2014). [PDF]
Jack Poulson, Laurent Demanet, Nicholas Maxwell, and Lexing Ying. A parallel butterfly algorithm. SIAM Journal on Scientific Computing 36 (2014). [PDF]
Paul Tsuji, Jack Poulson, Bjorn Engquist, and Lexing Ying. Sweeping preconditioners for elastic wave propagation with spectral element methods. ESAIM: Mathematical Modeling and Numerical Analysis 48 (2014). [PDF]
Phillip Schmitz and Lexing Ying. A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices. Journal of Computational Physics 258 (2014). [PDF]
Haizhao Yang and Lexing Ying. Synchrosqueezed wave packet transform for 2D mode decomposition. SIAM Journal on Imaging Sciences 6 (2014). [PDF]
Jingwei Hu, Sergey Fomel, Laurent Demanet, and Lexing Ying. A fast butterfly algorithm for the hyperbolic Radon transform. Geophysics 78 (2013). [PDF]
Jack Poulson, Bjorn Engquist, S. Li and Lexing Ying. A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations. SIAM Journal on Scientific Computing 35 (2013). [PDF]
X. Song, Sergey Fomel, and Lexing Ying. Lowrank finite-differences and lowrank Fourier finite-differences for seismic wave extrapolation. Geophysical Journal International 193 (2013). [PDF]
G. Bao, J. Qian, Lexing Ying, and H. Zhang. A convergent multiscale Gaussian-beam parametrix for wave equations. Communications in Partial Differential Equations 38 (2013). [PDF]
Bjorn Engquist and Lexing Ying. A fast algorithm for reiterated homogenization. Communications in Mathematical Sciences 11 (2013). [PDF]
Sergey Fomel, Lexing Ying, and X. Song. Seismic wave extrapolation using lowrank symbol approximation. Geophysical Prospecting 61 (2013). [PDF]
Lin Lin and Lexing Ying. Element orbitals for Kohn-Sham density functional theory. Physical Review B 85 (2012). [PDF]
I. Lashuk, A. Chandramowlishwaran, H. Langston, T. Nguyen, R. Sampath, A. Shringarpure, R. Vuduc, Lexing Ying, D. Zorin, and G. Biros. A massively parallel adaptive fast multipole method on heterogeneous architectures. Communications of the ACM 55 (2012). [PDF]
Lin Lin, Jianfeng Lu, Lexing Ying, and Weinan E. Optimized local basis set for Kohn-Sham density functional theory. Journal of Computational Physics 231 (2012). [PDF]
Haizhao Yang and Lexing Ying. A fast algorithm for multilinear operators. Applied and Computational Harmonic Analysis 33 (2012). [PDF]
Lexing Ying. A pedestrian introduction to fast multipole methods. Science China Mathematics 55 (2012). [PDF]
Laurent Demanet and L. Ying, Fast wave computation via Fourier integral operators. Mathematics of Computation 81 (2012). [PDF]
Paul Tsuji, Bjorn Engquist, and Lexing Ying. A sweeping preconditioner for time-harmonic Maxwell's equations with finite elements. Journal of Computational Physics 231 (2012). [PDF]
Paul Tsuji and Lexing Ying. A sweeping preconditioner for Yee's finite difference approximation of time-harmonic Maxwell's equations. Frontiers of Mathematics in China 7 (2012). [PDF]
Lin Lin, Jianfeng Lu, Lexing Ying, and Weinan E. Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation. Journal of Computational Physics 231 (2012). [PDF]
Laurent Demanet, M. Ferrara, N. Maxwell, Jack Poulson, and Lexing Ying. A butterfly algorithm for synthetic aperture radar imaging. SIAM Journal on Imaging Sciences 5 (2012). [PDF]
Jingwei Hu and Lexing Ying. A fast spectral algorithm for the quantum Boltzmann collision operator. Commun. Math. Sci 10 (2012). [PDF]
Phillip Schmitz and Lexing Ying. A fast direct solver for elliptic problems on general meshes in 2D. Journal of Computational Physics 231 (2012). [PDF]
Shidong Jiang, Bo Ren, Paul Tsuji, and Lexing Ying. Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions. Journal of Computational Physics 230 (2011). [PDF]
Bjorn Engquist and Lexing Ying. Sweeping preconditioner for the Helmholtz equation: Moving perfectly matched layers. SIAM Multiscale Modeling and Simulation 9 (2011). [PDF]
Lin Lin, Chao Yang, Jianfeng Lu, Lexing Ying, and Weinan E. A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations. SIAM Journal on Scientific Computing 33 (2011). [PDF]
Lin Lin, Jianfeng Lu, and Lexing Ying. Fast construction of hierarchical matrix representation from matrix-vector multiplication. Journal of Computational Physics 230 (2011). [PDF]
Paul Tsuji and Lexing Ying. A fast directional algorithm for high-frequency electromagnetic scattering. Journal of Computational Physics 230 (2011). [PDF]
Bjorn Engquist and Lexing Ying. Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation. Communications in Pure and Applied Mathematics 64 (2011). [PDF]
Lin Lin, C. Yang, Juan Meza, Jianfeng Lu, Lexing Ying, and Weinan E. SelInv--an algorithm for selected inversion of a sparse symmetric matrix. ACM Trans. Math. Software 37 (2011). [PDF]
Paul Tsuji, Dongbin Xiu, and Lexing Ying. A fast method for high-frequency acoustic scattering from random scatterers. International Journal on Uncertainty Quantification 1 (2011). [PDF]
Laurent Demanet and Lexing Ying. Discrete symbol calculus. SIAM Rev. 53 (2011). [PDF]
Jianliang Qian and Lexing Ying. Fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beams for the wave equation. SIAM Multiscale Modeling and Simulation 8 (2010). [PDF]
Jianliang Qian and Lexing Ying. Fast Gaussian wavepacket transforms and Gaussian beams for the Schrodinger equation. J. Computational Physics 229 (2010). [PDF]
Laurent Demanet and Lexing Ying. Scattering in flatland: efficient representations via wave atoms. Found. of Comput. Math. 10 (2010). [PDF]
Bjorn Engquist and Lexing Ying. Fast directional algorithms for the Helmholtz kernel. Journal of Computational and Applied Mathematics 234 (2010). [PDF]
Lin Lin, Jianfeng Lu, Lexing Ying. and Weinan E. Pole-based approximation of the Fermi-Dirac function. Chinese Annals of Mathematics - Series B 30 (2009). [PDF]
Lexing Ying and Sergey Fomel. Fast computation of partial Fourier transforms. SIAM Multiscale Modeling and Simulation 8 (2009). [PDF]
Lin Lin, Jianfeng Lu, Lexing Ying, Roberto Car, and Weinan E. Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems. Commun. Math. Sci. 7 (2009). [PDF]
Emmanuel Candes, Laurent Demanet and Lexing Ying. A fast butterfly algorithm for the computation of Fourier integral operators. SIAM Multiscale Modeling and Simulation 7 (2009). [PDF]
Bjorn Engquist and Lexing Ying. A fast directional algorithm for high frequency acoustic scattering in two dimension. Communications in Mathematical Sciences 7 (2009). [PDF]
Laurent Demanet and Lexing Ying. Wave atoms and time upscaling of wave equations. Numerische Mathematik 113 (2009). [PDF]
Lexing Ying. Sparse Fourier transform via butterfly algorithm. SIAM Journal on Scientific Computing 31 (2009). [PDF]
Laurent Demanet and Lexing Ying. Wave atoms and sparsity of oscillatory patterns. Applied and Computational Harmonic Analysis 23 (2007). [PDF]
Emmanuel Candes, Laurent Demanet and Lexing Ying. Fast computation of Fourier integral operators. SIAM Journal on Scientific Computing 29 (2007). [PDF]
Bjorn Engquist and Lexing Ying. Fast directional multilevel algorithms for oscillatory kernels. SIAM Journal on Scientific Computing 29 (2007). [PDF]
Lexing Ying and Emmanuel Candes. The phase flow method. Journal of Computational Physics 220 (2006). [PDF]
Lexing Ying and Emmanuel Candes. Fast geodesics computation with the phase flow method. Journal of Computational Physics 220 (2006). [PDF]
Lexing Ying, George Biros, and Denis Zorin. A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains. Journal of Computational Physics 219 (2006). [PDF]
Emmanuel Candes, Laurent Demanet, Donoho Donoho, and Lexing Ying. Fast discrete curvelet transforms. SIAM Multiscale Modeling and Simulation 5 (2006). [PDF]
Lexing Ying. A kernel independent fast multipole algorithm for radial basis functions. Journal of Computational Physics 213 (2006). [PDF]
Lexing Ying and Denis Zorin. A simple manifold-based construction of surfaces of arbitrary smoothness. ACM Transactions on Graphics 23 (2004) (SIGGRAPH 2004). [PDF]
Lexing Ying, George Biros, and Denis Zorin. A kernel-independent adaptive fast multipole method in two and three dimensions. Journal of Computational Physics 196 (2004). [PDF]
George Biros, Lexing Ying, and Denis Zorin. A fast solver for the Stokes equations with distributed forces in complex geometries. Journal of Computational Physics 194 (2004). [PDF]
L. Velho, K. Perlin, Lexing Ying, and H. Biermann. Algorithmic shape modeling with subdivision surfaces. Computers and Graphics 26 (2002). [PDF]

Older Refereed Conference Papers

Jingwei Hu, Sergey Fomel, and Lexing Ying. A fast algorithm for 3D azimuthally anisotropic velocity scan. Proceedings of the 2013 SEG Annual Meeting.
Jingwei Hu, Sergey Fomel, Laurent Demanet, and Lexing Ying. A fast butterfly algorithm for the hyperbolic Radon transform. Proceedings of the 2012 SEG Annual Meeting.
Jack Poulson, Bjorn Engquist, S. Li, and Lexing Ying. A parallel sweeping preconditioner for frequency-domain seismic wave propagation. Proceedings of the 2012 SEG Annual Meeting.
X. Song, Sergey Fomel, Lexing Ying, and T. Ding, Lowrank finite-difference for wave extrapolation. Proceedings of the 2011 SEG Annaul Meeting.
Bjorn Engquist, Jack Poulson, and Lexing Ying. Sweeping preconditioner for the 3D Helmholtz equation. Proceedings of the 2011 SEG Annaul Meeting.
Sergey Fomel, Lexing Ying, and X. Song, Seismic wave extrapolation using lowrank symbol approximation. Proceedings of the 2010 SEG Annaul Meeting.
I. Lashuk, A. Chandramowlishwaran, H. Langston, T. Nguyen, R. Sampath, A. Shringarpure, R. Vuduc, Lexing Ying, D. Zorin, and G. Biros. A massively parallel adaptive fast multipole method on heterogeneous architectures. Proceedings of Proc. ACM/IEEE Conf. Supercomputing (SC), Portland, OR, USA, 2009. This paper is nominated for the Best Technical Paper Award. [PDF]
Bjorn Engquist, Khoa Tran, and Lexing Ying. Fast hybrid algorithms for high frequency scattering Engquist. The 3rd Conference on Mathematical Modeling of Wave Phenomena and the 20th Nordic Conference on Radio Science and Communications. AIP Conference Proceedings, Volume 1106, pp. 3-17 (2009).
Laurent Demanet and Lexing Ying. Curvelets and wave atoms for mirror-extended images. Proc. SPIE Wavelets XII conf, San Diego, August 2007 (Invited Paper). [PDF]
Lexing Ying, Laurent Demanet, and Emmanuel Candes. 3D discrete curvelet transform. Proc. Wavelets XI conf., San Diego, July 2005 (Invited Paper). [PDF]
Lexing Ying, George Biros, Denis Zorin, and H. Langston. A new parallel kernel-independent fast multipole method. Proceedings of the 2003 ACM/IEEE conference on Supercomputing, 14-29, 2003. This paper was awarded the Best Student Paper Award and nominated for the Gordon Bell Award and the Best Technical Paper Award. [PDF]
George Biros, Lexing Ying, Denis Zorin. The embedded boundary integral equation solver for the incompressible Navier-Stokes equations. International Association for Boundary Element Methods Symposium, 2002. [PDF]
Lexing Ying, Denis Zorin. Nonmanifold subdivision. The 12th IEEE Visualization Conference, 2001. [PDF]
Lexing Ying, A. Hertzmann, H. Biermann, Denis Zorin. Texture and shape synthesis on surfaces. The 12th Eurographics Workshop on Rendering, 2001. [PDF]

Book Chapters

Bjorn Engquist and Lexing Ying. Fast algorithms for high frequency wave propagation. Numerical Analysis of Multiscale Problems, I. Graham, T. Hou, O. Lakkis and R. Scheichl (editors), Lecture Notes in Computational Science and Engineeering, Springer.
Lexing Ying. Fast algorithms boundary integral equations. In Bjorn Engquist, O. Runborg, P. Lotstedt, editors, Multiscale Methods in Science and Engineering, pages 139-194, volume 66 of Lecture Notes in Computational Science and Engineering, Heidelberg, 2009. Springer Verlag. [PDF]

Techincal Reports

Anshul Gupta and Lexing Ying. A Fast Maximum-Weight-Bipartite-Matching Algorithm for Reducing Pivoting in Sparse Gaussian Elimination. Technical report RC 21576 (97320), IBM T. J. Watson Research Center, Yorktown Heights, NY, 1999. [PDF]

Software

Eigenmatrix for unstructured sparse recovery. [Code]
Stable factorization for phase factors of quantum signal processing [Code]
Sweeping preconditioner [Code]
Additive sweeping preconditioner [Code]
Recursive sweeping preconditioner [Code]
1D synchrosqueezed wave packet transforms [Code]
Multiscale Butterfly Algorithm [Code]
Butterfly factorization [Code]
ButterflyLab [Code]
Directional FMM (3D parallel) for Helmholtz Equation [Code]
Directional FMM (3D sequential) for Helmholtz Equation [Code]
Directional FMM (2D sequential) for Helmholtz Equation [Code]
Wave atom transforms [Code]
Fast discrete Curvelet transform [Code]
Manifold-based surface construction of arbitrary smoothness [Code]
Kernel independent fast multipole method [Code]