- F. Liu and L. Ying. Sparsify and sweep: an efficient preconditioner for the Lippmann-Schwinger equation. Submitted. [PDF]
- Z. Cai, Y. Fan, and L. Ying. Entropy monotonic spectral method for Boltzmann equation. Submitted. [PDF]
- A. Damle, V. Minden, and L. Ying. Robust and efficient multi-way spectral clustering. Submitted. [PDF]
- A. Damle, L. Lin, and L. Ying. Accelerating selected columns of the density matrix computations via approximate column selection. Submitted. [PDF]
- V. Minden, A. Damle, K. Ho, and L. Ying. Fast spatial Gaussian process maximum likelihood estimation via skeletonization factorizations. Submitted. [PDF]

- L. Ying. Tensor network skeletonization. To appear in SIAM Multiscale Modeling and Simulation. [PDF]
- Y. Li, H. Yang, and L. Ying. Multidimensional butterfly factorization. To appear in Applied and Computational Harmonic Analysis. [PDF]
- Y. Li and L. Ying. Distributed-memory hierarchical interpolative factorization. To appear in Research in Mathematical Sciences. [PDF]
- F. Liu and L. Ying. Localized sparsifying preconditioner for periodic indefinite systems. Communications in Mathematical Sciences 15-4 (2017). [PDF]
- V. Minden, K. L. Ho, A. Damle, and L. Ying. A recursive skeletonization factorization based on strong admissibility. SIAM Multiscale Modeling and Simulation 15-2 (2017). [PDF]
- L. Lin, Z. Xu, and L. Ying. Adaptively compressed polarizability operator for accelerating large scale ab initio phonon calculations. SIAM Multiscale Modeling and Simulation 15-1 (2017). [PDF]
- A. Damle, L. Lin, and L. Ying. SCDM-k: Localized orbitals for solids via selected columns of the density matrix. Journal of Computational Physics 334 (2017). [PDF]
- J. Lu and L. Ying, Fast algorithm for periodic density fitting for Bloch waves. Annals of Mathematical Sciences and Applications 1-2 (2016). [PDF]
- J. Lu and L. Ying, Sparsifying preconditioner for soliton calculations. Journal of Computational Physics 315 (2016). [PDF]
- F. Liu and L. Ying. Additive sweeping preconditioner for the Helmholtz equation. SIAM Multiscale Modeling and Simulation 14-2 (2016). [PDF]
- F. Liu and L. Ying. Recursive sweeping preconditioner for the 3D Helmholtz equation. SIAM Journal on Scientific Computing 38-2 (2016). [PDF]
- V. Minden, A. Damle, K. Ho, and L. Ying. A technique for updating hierarchical factorizations of integral operators. SIAM Multiscale Modeling and Simulation 14-1 (2016). [PDF]
- J. Sun, S. Fomel, and L. Ying. Lowrank one-step wave extrapolation for reverse-time migration. Geophysics 81-1 (2016).
- K. Ho and L. Ying. Hierarchical interpolative factorization for elliptic operators: differential equations. Communications in Pure and Applied Mathematics 69-8 (2016). [PDF]
- K. Ho and L. Ying. Hierarchical interpolative factorization for elliptic operators: integral equations. Communications in Pure and Applied Mathematics 69-7 (2016). [PDF]
- H. Yang, J. Lu, and L. Ying. Crystal image analysis using 2D synchrosqueezed transforms. SIAM Multiscale Modeling and Simulation 13-4 (2015). [PDF]
- J. Lu and L. Ying. Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost. Journal of Computational Physics 302-1 (2015). [PDF]
- L. Ying. Directional preconditioner for 2D high frequency obstacle scattering. SIAM Multiscale Modeling and Simulation 13-3 (2015). [PDF]
- H. Yang, J. Lu, W. Brown, I. Daubechies, and L. Ying. Quantitative canvas weave analysis using 2D synchrosqueezed transforms. IEEE Signal Processing Magazine 55 (2015). [PDF]
- Y. Li, H. Yang, E. Martin, K. Ho, and L. Ying. Butterfly factorization. SIAM Multiscale Modeling and Simulation 13-2 (2015). [PDF]
- L. Ying. Sparsifying preconditioner for the Lippmann-Schwinger equation. SIAM Multiscale Modeling and Simulation 13-2 (2015). [PDF]
- Y. Li, H. Yang, and L. Ying. A multiscale butterfly algorithm for multidimensional Fourier integral operators. SIAM Multiscale Modeling and Simulation 13-2 (2015). [PDF]
- A. Damle, L. Lin, and L. Ying. Compressed representation of Kohn-Sham orbitals via selected columns of the density matrix. J. Chem. Theory Comput. 11 (2015) [PDF]
- L. Ying. Sparsifying preconditioner for pseudospectral approximations of indefinite systems on periodic structures. SIAM Multiscale Modeling and Simulation 13-2 (2015). [PDF]
- L. Ying. Fast directional computation of high frequency boundary integrals via local FFTs. SIAM Multiscale Modeling and Simulation 13-1 (2015). [PDF]
- J. Hu and L. Ying, A fast algorithm for the energy space boson Boltzmann collision operator. Mathematics of Computation 84 (2015). [PDF]
- J. Hu, S. Fomel, and L. Ying. A fast algorithm for 3D azimuthally anisotropic velocity scan. Geophysical Prospecting 63 (2015). [PDF]
- A. Damle, L. Lin, and L. Ying. Pole expansion for solving a type of parametrized linear systems in electronic structure calculations. SIAM Journal on Scientific Computing 36 (2014). [PDF]
- A. Benson, J. Poulson, K. Tran, B. Engquist, and L. Ying. A parallel directional fast multipole method. SIAM Journal on Scientific Computing 36 (2014). [PDF]
- H. Yang and L. Ying, Synchrosqueezed curvelet transform for two-dimensional mode decomposition. SIAM Journal on Mathematical Analysis 46 (2014). [PDF]
- J. Poulson, L. Demanet, N. Maxwell, and L. Ying. A parallel butterfly algorithm. SIAM Journal on Scientific Computing 36 (2014). [PDF]
- P. Tsuji, J. Poulson, B. Engquist, and L. Ying. Sweeping preconditioners for elastic wave propagation with spectral element methods. ESAIM: Mathematical Modeling and Numerical Analysis 48 (2014). [PDF]
- P. Schmitz and L. Ying. A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices. Journal of Computational Physics 258 (2014). [PDF]
- H. Yang and L. Ying. Synchrosqueezed wave packet transform for 2D mode decomposition. SIAM Journal on Imaging Sciences 6 (2014). [PDF]
- J. Hu, S. Fomel, L. Demanet, and L. Ying. A fast butterfly algorithm for the hyperbolic Radon transform. Geophysics 78 (2013). [PDF]
- J. Poulson, B. Engquist, S. Li and L. Ying. A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations. SIAM Journal on Scientific Computing 35 (2013). [PDF]
- X. Song, S. Fomel, and L. Ying. Lowrank finite-differences and lowrank Fourier finite-differences for seismic wave extrapolation. Geophysical Journal International 193 (2013). [PDF]
- G. Bao, J. Qian, L. Ying, and H. Zhang. A convergent multiscale Gaussian-beam parametrix for wave equations. Communications in Partial Differential Equations 38 (2013). [PDF]
- B. Engquist and L. Ying. A fast algorithm for reiterated homogenization. Communications in Mathematical Sciences 11 (2013). [PDF]
- S. Fomel, L. Ying, and X. Song. Seismic wave extrapolation using lowrank symbol approximation. Geophysical Prospecting 61 (2013). [PDF]
- L. Lin and L. 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, L. Ying, D. Zorin, and G. Biros. A massively parallel adaptive fast multipole method on heterogeneous architectures. Communications of the ACM 55 (2012). [PDF]
- L. Lin, J. Lu, L. Ying, and W. E. Optimized local basis set for Kohn-Sham density functional theory. Journal of Computational Physics 231 (2012). [PDF]
- H. Yang and L. Ying. A fast algorithm for multilinear operators. Applied and Computational Harmonic Analysis 33 (2012). [PDF]
- L. Ying. A pedestrian introduction to fast multipole methods. Science China Mathematics 55 (2012). [PDF]
- L. Demanet and L. Ying. Fast wave computation via Fourier integral operators. Mathematics of Computation 81 (2012). [PDF]
- P. Tsuji, B. Engquist, and L. Ying. A sweeping preconditioner for time-harmonic Maxwell's equations with finite elements. Journal of Computational Physics 231 (2012). [PDF]
- P. Tsuji and L. Ying. A sweeping preconditioner for Yee's finite difference approximation of time-harmonic Maxwell's equations. Frontiers of Mathematics in China 7 (2012). [PDF]
- L. Lin, J. Lu, L. Ying, and W. 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]
- L. Demanet, M. Ferrara, N. Maxwell, J. Poulson, and L. Ying. A butterfly algorithm for synthetic aperture radar imaging. SIAM Journal on Imaging Sciences 5 (2012). [PDF]
- J. Hu and L. Ying. A fast spectral algorithm for the quantum Boltzmann collision operator. Commun. Math. Sci 10 (2012). [PDF]
- P. Schmitz and L. Ying. A fast direct solver for elliptic problems on general meshes in 2D. Journal of Computational Physics 231 (2012). [PDF]
- S. Jiang, B. Ren, P. Tsuji, and L. 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]
- B. Engquist and L. Ying. Sweeping preconditioner for the Helmholtz equation: Moving perfectly matched layers. SIAM Multiscale Modeling and Simulation 9 (2011). [PDF]
- L. Lin, C. Yang, J. Lu, L. Ying, and W. 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]
- L. Lin, J. Lu, and L. Ying. Fast construction of hierarchical matrix representation from matrix-vector multiplication. Journal of Computational Physics 230 (2011). [PDF]
- P. Tsuji and L. Ying. A fast directional algorithm for high-frequency electromagnetic scattering. Journal of Computational Physics 230 (2011). [PDF]
- B. Engquist and L. Ying. Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation. Communications in Pure and Applied Mathematics 64 (2011). [PDF]
- L. Lin, C. Yang, J. Meza, J. Lu, L. Ying, and W. E. SelInv--an algorithm for selected inversion of a sparse symmetric matrix. ACM Trans. Math. Software 37 (2011). [PDF]
- P. Tsuji, D. Xiu, and L. Ying. A fast method for high-frequency acoustic scattering from random scatterers. International Journal on Uncertainty Quantification 1 (2011). [PDF]
- L. Demanet and L. Ying. Discrete symbol calculus. SIAM Rev. 53 (2011). [PDF]
- J. Qian and L. Ying. Fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beams for the wave equation. SIAM Multiscale Modeling and Simulation 8 (2010). [PDF]
- J. Qian and L. Ying. Fast Gaussian wavepacket transforms and Gaussian beams for the Schrodinger equation. J. Computational Physics 229 (2010). [PDF]
- L. Demanet and L. Ying. Scattering in flatland: efficient representations via wave atoms. Found. of Comput. Math. 10 (2010). [PDF]
- B. Engquist and L. Ying. Fast directional algorithms for the Helmholtz kernel. Journal of Computational and Applied Mathematics 234 (2010). [PDF]
- L. Lin, J. Lu, L. Ying, and W. E. Pole-based approximation of the Fermi-Dirac function. Chinese Annals of Mathematics - Series B 30 (2009). [PDF]
- L. Ying and S. Fomel. Fast computation of partial Fourier transforms. SIAM Multiscale Modeling and Simulation 8 (2009). [PDF]
- L. Lin, J. Lu, L. Ying, R. Car, and W. 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]
- E. Candes, L. Demanet and L. Ying. A fast butterfly algorithm for the computation of Fourier integral operators. SIAM Multiscale Modeling and Simulation 7 (2009). [PDF]
- B. Engquist and L. Ying. A fast directional algorithm for high frequency acoustic scattering in two dimension. Communications in Mathematical Sciences 7 (2009). [PDF]
- L. Demanet and L. Ying. Wave atoms and time upscaling of wave equations. Numerische Mathematik 113 (2009). [PDF]
- L. Ying. Sparse Fourier transform via butterfly algorithm. SIAM Journal on Scientific Computing 31 (2009). [PDF]
- L. Demanet and L. Ying. Wave atoms and sparsity of oscillatory patterns. Applied and Computational Harmonic Analysis 23 (2007). [PDF] [CODE]
- E. Candes, L. Demanet and L. Ying. Fast computation of Fourier integral operators. SIAM Journal on Scientific Computing 29 (2007). [PDF]
- B. Engquist and L. Ying. Fast directional multilevel algorithms for oscillatory kernels. SIAM Journal on Scientific Computing 29 (2007). [PDF]
- L. Ying and E. Candes. The phase flow method. Journal of Computational Physics 220 (2006). [PDF]
- L. Ying and E. Candes. Fast geodesics computation with the phase flow method. Journal of Computational Physics 220 (2006). [PDF]
- L. Ying, G. Biros, and D. Zorin. A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains. Journal of Computational Physics 219 (2006). [PDF]
- E. Candes, L. Demanet, D. Donoho, and L. Ying. Fast discrete curvelet transforms. SIAM Multiscale Modeling and Simulation 5 (2006). [PDF] [CODE]
- L. Ying. A kernel independent fast multipole algorithm for radial basis functions. Journal of Computational Physics 213 (2006). [PDF]
- L. Ying and D. Zorin. A simple manifold-based construction of surfaces of arbitrary smoothness. ACM Transactions on Graphics 23 (2004) (SIGGRAPH 2004). [PDF] [CODE]
- L. Ying, G. Biros, and D. Zorin. A kernel-independent adaptive fast multipole method in two and three dimensions. Journal of Computational Physics 196 (2004). [PDF] [CODE]
- G. Biros, L. Ying, and D. 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, L. Ying, and H. Biermann. Algorithmic shape modeling with subdivision surfaces. Computers and Graphics 26 (2002). [PDF]

- B. Engquist and L. Ying, Fast algorithms for high frequency wave propagation. To appear in Numerical Analysis of Multiscale Problems, I. Graham, T. Hou, O. Lakkis and R. Scheichl (editors), Lecture Notes in Computational Science and Engineeering, Springer.
- L. Ying. Fast algorithms for boundary integral equations. In B. 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]

- J. Hu, S. Fomel, and L. Ying, A fast algorithm for 3D azimuthally anisotropic velocity scan. Proceedings of the 2013 SEG Annual Meeting.
- J. Hu, S. Fomel, L. Demanet, and L. Ying, A fast butterfly algorithm for the hyperbolic Radon transform. Proceedings of the 2012 SEG Annual Meeting.
- J. Poulson, B. Engquist, S. Li, and L. Ying, A parallel sweeping preconditioner for frequency-domain seismic wave propagation. Proceedings of the 2012 SEG Annual Meeting.
- X. Song, S. Fomel, L. Ying, and T. Ding, Lowrank finite-difference for wave extrapolation. Proceedings of the 2011 SEG Annaul Meeting.
- B. Engquist, J. Poulson, and L. Ying, Sweeping preconditioner for the 3D Helmholtz equation. Proceedings of the 2011 SEG Annaul Meeting.
- S. Fomel, L. 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, L. 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]
- B. Engquist, K. Tran, and L. 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).
- L. Demanet and L. Ying. Curvelets and wave atoms for mirror-extended images. Proc. SPIE Wavelets XII conf, San Diego, August 2007 (Invited Paper). [PDF] [CODE]
- L. Ying, L. Demanet, and E. Candes. 3D discrete curvelet transform. Proc. Wavelets XI conf., San Diego, July 2005 (Invited Paper). [PDF]
- L. Ying, G. Biros, D. 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]
- G. Biros, L. Ying, D. Zorin. The embedded boundary integral equation solver for the incompressible Navier-Stokes equations. International Association for Boundary Element Methods Symposium, 2002. [PDF]
- L. Ying, D. Zorin. Nonmanifold subdivision. The 12th IEEE Visualization Conference, 2001. [PDF]
- L. Ying, A. Hertzmann, H. Biermann, D. Zorin. Texture and shape synthesis on surfaces. The 12th Eurographics Workshop on Rendering, 2001. [PDF]

- A. Gupta and L. 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]