• Milestones in Matrix Computation: Selected Works of Gene H. Golub, with Commentaries [webpage]
  Raymond H. Chan, Chen Greif, and Dianne P. O'Leary, eds.
  Oxford University Press, 2007
  

Recent Reports and Refereed Journal Publications

• Monolithic Multigrid for the Marker-and-Cell Discretization of the Stokes-Darcy Equations [pdf]
  Chen Greif and Yunhui He, Journal of Computational and Applied Mathematics, 463:116518, 2025

• On the Invertibility of Matrices with a Double Saddle-Point Structure [pdf]
  Fatemeh P.A. Beik, Chen Greif, and Manfred Trummer, Linear Algebra and its Applications, 699:403-420, 2024
  

• Augmentation-Based Preconditioners for Saddle-Point Systems with Singular Leading Blocks [pdf]
  Susanne Bradley and Chen Greif, Electronic Transactions on Numerical Analysis, 60:221-237, 2024
  

• Incomplete double-cone factorizations of centrosymmetric matrices arising in spectral methods [pdf]
  Chen Greif, Sarah Nataj, and Manfred Trummer, Numerical Algorithms 95(3):1359-1386, 2024
  

• Block Preconditioners for the Marker-and-Cell Discretization of the Stokes-Darcy Equations [pdf] (comments)
  Chen Greif and Yunhui He, SIAM Journal on Matrix Analysis and Applications, 44(4):1540-1565, 2023
  

• A closed-form Multigrid Smoothing Factor for an Additive Vanka-Type Smoother Applied to the Poisson Equation [pdf]
  Chen Greif and Yunhui He, Numerical Linear Algebra with Applications, 2023
  

• Eigenvalue Bounds for Saddle-Point Systems with Singular Leading Blocks [pdf]
  Susanne Bradley and Chen Greif, Journal of Computational and Applied Mathematics 424, 2023
  

• Eigenvalue Bounds for Double Saddle-Point Systems [pdf]
  Susanne Bradley and Chen Greif, IMA Journal of Numerical Analysis, 43:3564-3592, 2023
  

• Structured Shifts for Skew-Symmetric Matrices [pdf]
  Chen Greif, Electronic Transactions on Numerical Analysis, 55:455-468, 2022
  

• Optimal Complex Relaxation Parameters in Multigrid for Complex-Shifted Linear Systems [pdf] [code]
  Robert Hocking and Chen Greif
  SIAM Journal on Matrix Analysis and Applications, 42(2):475-502, 2021
  

• A Scalable Approximate Inverse Block Preconditioner for an Incompressible Magnetohydrodynamics Model Problem [pdf]
  Michael Wathen and Chen Greif
  SIAM Journal on Scientific Computing, 42(1):B57-B79, 2020
  

• Conjugate Gradient for Nonsingular Saddle-Point Systems with a Maximally Rank-Deficient Leading Block [pdf]
  Chen Greif and Michael Wathen
  Journal of Computational and Applied Mathematics, 358:1-11, 2019
  

• SPMR: a Family of Saddle-Point Minimum Residual Solvers [pdf]
  Ron Estrin and Chen Greif
  SIAM Journal on Scientific Computing, 40(3), A1884-A1914, 2018
  

• Mstab: Stabilized Reduced Dimension Reduction for Krylov Subspace Recycling [pdf]
  Martin Neuenhofen and Chen Greif
  SIAM Journal on Scientific Computing, 40(2):B554-B571, 2018
  

• Preconditioners for Mixed Finite Element Discretizations of Incompressible MHD Equations [pdf]
  Michael Wathen, Chen Greif, and Dominik Schötzau
  SIAM Journal on Scientific Computing, 39(6):A2293-A3013, 2017
  

• Numerical Solution of Linear Eigenvalue Problems [pdf]
  Jessica Bosch and Chen Greif
  Contemporary Mathematics, 700:117-153, 2017
  

• SYM-ILDL: Incomplete LDL^T Factorization of Symmetric Indefinite and Skew-Symmetric Matrices [pdf] [code]
  Chen Greif, Shiwen He, and Paul Liu
  ACM Transactions on Mathematical Software, 44(1):1-21, 2017
  

• Dip Transform for 3D Shape Reconstruction [pdf]
  Kfir Aberman, Oren Katzir, Qiang Zhou, Zegang Luo, Andrei Sharf, Chen Greif, Baoquan Chen, and Daniel Cohen-Or
  ACM Transactions on Graphics (Special Issue of SIGGRAPH), 36:4 (Article 79), 2017
  

• A Stabilized Multigrid Solver for Hyperelastic Image Registration [pdf]
  Lars Ruthotto, Chen Greif, and Jan Modersitski
  Numerical Linear Algebra with Applications, 24(5), e2095, 2017
  

• GMRES with Multiple Preconditioners [pdf]
  Chen Greif, Tyrone Rees, and Daniel Szyld
  Boletin de la Sociedad Espanola de Matematica Aplicada (SeMA), 74(2):213-231, 2017
  

• Numerical Equivalences among Iterative Algorithms for Skew-Symmetric Matrices [pdf]
  Chen Greif, Chris Paige, David Titley-Peloquin, and Jim Varah
  SIAM Journal on Matrix Analysis and Applications, 37(3):1071-1087, 2016
  

• Towards an Optimal Condition Number of Certain Augmented Lagrangian-type Saddle-Point Matrices [pdf]
  Ron Estrin and Chen Greif
  Numerical Linear Algebra with Applications, 23:693-705, 2016
  

• On Nonsingular Saddle-Point Systems with a Maximally Rank-Deficient Leading Block [pdf]
  Ron Estrin and Chen Greif
  SIAM Journal on Matrix Analysis and Applications, 36(2):367-384, 2015
  

• Simulating Rigid Body Fracture with Surface Meshes [pdf]
  Yufeng Zhu, Robert Bridson, and Chen Greif
  ACM Transactions on Graphics (SIGGRAPH), 2015
  

• Restoring the Missing Vorticity in Advection-Projection Fluid Solvers [pdf]
  Xinxin Zhang, Robert Bridson, and Chen Greif
  ACM Transactions on Graphics (SIGGRAPH), 2015
  

• Bounds on Eigenvalues of Matrices Arising from Interior-Point Methods [pdf]
  Chen Greif, Erin Moulding, and Dominique Orban
  SIAM Journal on Optimization, 24(1):49-83, 2014
  

• Additive Schwarz with Variable Weights [pdf]
  Chen Greif, Tyrone Rees, and Daniel Szyld
  Proceedings of the 21st International Conference on Domain Decomposition Methods. Lecture Notes in Computer Science and Engineering, Springer, Berlin and Heidelberg, 655-662, 2014
  

• The Power and Arnoldi Methods in an Algebra of Circulants [pdf] [code]
  David Gleich, Chen Greif, and Jim Varah
  Numerical Linear Algebra with Applications, 20(5):809-831, 2013
  

• Parallel Numerical Solution of the Time-Harmonic Maxwell Equations in Mixed Form [pdf]
  Dan Li, Chen Greif, and Dominik Schötzau
  Numerical Linear Algebra with Applications, 19(3): 525-539, 2012
  
  
• Fast Matrix Computations for Pair-Wise and Column-Wise Commute Times and Katz Scores [pdf]
  Francesco Bonchi, Pooya Esfandiar, David Gleich, Chen Greif, and Laks Lakshmanan
  Internet Mathematics, 8(1-2): 73-112, 2012
  
  
• Closed-Form Multigrid Smoothing Factors for Lexicographic Gauss-Seidel [pdf]
  Robert Hocking and Chen Greif
  IMA Journal of Numerical Analysis, 32(3): 795-812, 2012
  
  
• A Note on the Convergence of SOR for the PageRank Problem [pdf]
  Chen Greif and David Kurokawa
  SIAM Journal on Scientific Computing, 33(6): 3201-3209, 2011
  
  
• A Box-Shaped Cyclically Reduced Operator [pdf]
  Chen Greif and Robert Hocking
  Numerical Linear Algebra with Applications, 18(4): 671-693, 2011
  
  
• A Mixed Finite Element Method with Exactly Divergence-free Velocities for Incompressible Magnetohydrodynamics [pdf]
  Chen Greif, Dan Li, Dominik Schötzau, and Xiaoxi Wei
  Computer Methods in Applied Mechanics and Engineering, 199: 2840-2855, 2010
  
  
• An Analysis of Low-Rank Modifications of Preconditioners for Saddle Point Systems [pdf]
  Chen Greif and Michael Overton
  Electronic Transactions on Numerical Analysis, 37: 307-320, 2010
  
  
• l₁-Sparse Reconstruction of Sharp Point Set Surfaces [pdf]
  Haim Avron, Andrei Sharf, Chen Greif and Daniel Cohen-Or
  ACM Transactions on Graphics, 29(5): 135:1-135:12, 2010
  
  
• An Inner-Outer Iteration for Computing PageRank [pdf] [code]
  David Gleich, Andrew Gray, Chen Greif and Tracy Lau
  SIAM Journal on Scientific Computing, 32(1): 349-371, 2010
  
  
• Iterative Solution of Skew-Symmetric Linear Systems [pdf]
  Chen Greif and Jim Varah
  SIAM Journal on Matrix Analysis and Applications, 31(2): 584-601, 2009
  
  
• Space-time Surface Reconstruction Using Incompressible Flow [pdf]
  Andrei Sharf, Dan A. Alcantara, Thomas Lewiner, Chen Greif, Alla Sheffer, Nina Amenta, and Daniel Cohen-Or
  ACM Transactions on Graphics, 27(5), (SIGGRAPH Asia) 2008
  
  
• An Efficient Linear Programming Solver for Optimal Filter Synthesis [pdf]
  Jihong Ren, Chen Greif, and Mark Greenstreet
  Numerical Linear Algebra with Applications, 14(9): 695-712, 2007
  
  
• A Preconditioner for Linear Systems Arising from Interior Point Optimization Methods [pdf]
  Tim Rees and Chen Greif
  SIAM Journal on Scientific Computing, 29(5): 1992-2007, 2007
  
  
• Preconditioners for the Discretized Time-Harmonic Maxwell Equations in Mixed Form [pdf]
  Chen Greif and Dominik Schötzau
  Numerical Linear Algebra with Applications, 14(4): 281-297, 2007
  
  
• Minimizing the Condition Number for Small Rank Modifications [pdf]
  Chen Greif and Jim Varah
  SIAM Journal on Matrix Analysis and Applications, 29(1): 82-97, 2006
  
  
• An Arnoldi-type Algorithm for Computing PageRank [pdf]
  Gene Golub and Chen Greif
  BIT, 46(4): 759-771, 2006
  
  
• A Multipreconditioned Conjugate Gradient Algorithm [pdf] [code]
  Robert Bridson and Chen Greif
  SIAM Journal on Matrix Analysis and Applications, 27(4): 1056-1068, 2006
  
  
• Preconditioners for Saddle Point Linear Systems with Highly Singular (1,1) Blocks [pdf]
  Chen Greif and Dominik Schötzau
  Electronic Transactions on Numerical Analysis, 22: 114-121, 2006
  
  
• An Algebraic Analysis of a Block Diagonal Preconditioner for Saddle Point Systems [pdf]
  Gene Golub, Chen Greif, and Jim Varah
  SIAM Journal on Matrix Analysis and Applications, 27(3): 779-792, 2005
  
  
• Simultaneous Registration and Activation Detection for fMRI [pdf]
  Jeff Orchard, Chen Greif, Gene Golub, Bruce Bjornson, and M. Stella Atkins
  IEEE Transactions on Medical Imaging, 22(11):1427-1435, 2003
  
  
• On Solving Block-Structured Indefinite Linear Systems [pdf]
  Gene Golub and Chen Greif
  SIAM Journal on Scientific Computing, 24(6): 2076-2092, 2003
  
  
• Block Orderings for Tensor-Product Grids in Two and Three Dimensions [pdf]
  Gene Golub, Chen Greif, and Jim Varah
  Numerical Algorithms, 30(2): 93-111, 2002
  
  
• Reduced Systems for Three-Dimensional Elliptic Equations with Variable Coefficients [pdf]
  Chen Greif
  SIAM Journal on Matrix Analysis and Applications, 21(1): 29-44, 1999
  
  
• Block Stationary Methods for Nonsymmetric Cyclically Reduced Systems Arising from Three-Dimensional Elliptic Equations [pdf]
  Chen Greif and Jim Varah
  SIAM Journal on Matrix Analysis and Applications, 20(4): 1038-1059, 1999
  
  
• Iterative Solution of Cyclically Reduced Systems Arising from Discretization of the Three-Dimensional Convection-Diffusion Equation [pdf]
  Chen Greif and Jim Varah
  SIAM Journal on Scientific Computing, 19(6): 1018-1040, 1998
  
  
• The d₂-Transformation for Infinite Double Series and the D₂-Transformation for Infinite Double Integrals [pdf]
  Chen Greif and David Levin
  Mathematics of Computation, 67(222): 695-714, 1998