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- Gene H. Golub, Chen Greif
- SIAM J. Scientific Computing
- 2003

We introduce a new preconditioning technique for the iterative solution of saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioners are block diagonal and are based on augmentation, using symmetric positive definite weight matrices. If the nullity is equal to the number of constraints, the precon-ditioned matrices have… (More)

- Chen Greif, Dominik Schötzau
- Numerical Lin. Alg. with Applic.
- 2007

SUMMARY We introduce a new preconditioning technique for iteratively solving linear systems arising from finite element discretization of the mixed formulation of the time-harmonic Maxwell equations. The preconditioners are motivated by spectral equivalence properties of the discrete operators, but are augmentation-free and Schur complement-free. We provide… (More)

- Chen Greif, Erin Moulding, Dominique Orban
- SIAM Journal on Optimization
- 2014

Interior-point methods feature prominently among numerical methods for inequality-constrained optimization problems, and involve the need to solve a sequence of linear systems that typically become increasingly ill-conditioned with the iterations. To solve these systems, whose original form has a nonsymmetric 3×3 block structure, it is common practice to… (More)

- A M Díez-Navajas, S Wiedemann-Merdinoglu, C Greif, D Merdinoglu
- Phytopathology
- 2008

Following inoculation of host and nonhost plants with Plasmopara viticola, the grapevine downy mildew, a histological survey was undertaken to identify the stage where its development is contained in nonhosts and in resistant host plants. Three herbaceous nonhost species, Beta vulgaris, Lactuca sativa, and Capsicum annuum, and three grapevine species… (More)

We perform an algebraic analysis of a generalization of the augmented Lagrangian method for solution of saddle point linear systems. It is shown that in cases where the (1,1) block is singular, specifically semidefinite, a low-rank perturbation that minimizes the condition number of the perturbed matrix while maintaining sparsity is an effective approach.… (More)

- Haim Avron, Andrei Sharf, Chen Greif, Daniel Cohen-Or
- ACM Trans. Graph.
- 2010

We introduce an ℓ<sub>1</sub>-sparse method for the reconstruction of a piecewise smooth point set surface. The technique is motivated by recent advancements in sparse signal reconstruction. The assumption underlying our work is that common objects, even geometrically complex ones, can typically be characterized by a rather small number of features.… (More)

- Francesco Bonchi, Pooya Esfandiar, David F. Gleich, Chen Greif, Laks V. S. Lakshmanan
- Internet Mathematics
- 2012

We first explore methods for approximating the commute time and Katz score between a pair of nodes. These methods are based on the approach of matrices, moments , and quadrature developed in the numerical linear algebra community. They rely on the Lanczos process and provide upper and lower bounds on an estimate of the pair-wise scores. We also explore… (More)

- David F. Gleich, Peter W. Glynn, Gene H. Golub, Chen Greif
- Web Information Retrieval and Linear Algebra…
- 2007

The three results on the PageRank vector are preliminary but shed light on the eigenstructure of a PageRank modified Markov chain and what happens when changing the teleportation parameter in the PageRank model. Computations with the derivative of the PageRank vector with respect to the teleportation parameter show predictive ability and identify an… (More)

- Gene H. Golub, Chen Greif, James M. Varah
- SIAM J. Matrix Analysis Applications
- 2005

We consider a positive definite block preconditioner for solving saddle point linear systems. An approach based on augmenting the (1,1) block while keeping its condition number small is described, and algebraic analysis is performed. Ways of selecting the parameters involved are discussed, and analytical and numerical observations are given.