1.3k citations · 2.2k across the 67 of their papers we have counts for
17 papers · 1 filter
Fault Oblivious Eigenvalue Solver
Jayanta Mukherjee, Xuejiao Kang, David F. Gleich +2
Eigenvalue problems serve as fundamental substrates for applications in large-scale scientific simulations and machine learning, often requiring computation on massively parallel p…
Dominant H-Eigenvectors of Tensor Kronecker Products Do Not Decouple
Ayush Kulkarni, Charles Colley, David F. Gleich
We illustrate a counterexample to an open question related to the dominant H-eigenvector of a Kronecker product of tensors. For matrices and Z-eigenvectors of tensors, the dominant…
An Empirical Study of Conjugate Gradient Preconditioners for Solving Symmetric Positive Definite Systems of Linear Equations
Marc A. Tunnell, David F. Gleich
Despite hundreds of papers on preconditioned linear systems of equations, there remains a significant lack of comprehensive performance benchmarks comparing various preconditioners…
Better than best low-rank approximation with the singular value decomposition
David F. Gleich
The Eckhart-Young theorem states that the best low-rank approximation of a matrix can be constructed from the leading singular values and vectors of the matrix. Here, we illustrate…
A Projection Method for Metric-Constrained Optimization
Nate Veldt, David Gleich, Anthony Wirth +1
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give s…
Computing tensor Z-eigenvectors with dynamical systems
Austin R. Benson, David F. Gleich
We present a new framework for computing Z-eigenvectors of general tensors based on numerically integrating a dynamical system that can only converge to a Z-eigenvector. Our motiva…
Multi-way Monte Carlo Method for Linear Systems
Tao Wu, David F. Gleich
We study the Monte Carlo method for solving a linear system of the form . A sufficient condition for the method to work is , which greatly limits the usab…
A randomized algorithm for enumerating zonotope vertices
Kerrek Stinson, David F. Gleich, Paul G. Constantine
We propose a randomized algorithm for enumerating the vertices of a zonotope, which is a low-dimensional linear projection of a hypercube. The algorithm produces a pair of the zono…
The Spacey Random Walk: a Stochastic Process for Higher-order Data
Austin R. Benson, David F. Gleich, Lek-Heng Lim
Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the frac…
Erasure coding for fault oblivious linear system solvers
David F. Gleich, Ananth Grama, Yao Zhu
Dealing with hardware and software faults is an important problem as parallel and distributed systems scale to millions of processing cores and wide area networks. Traditional meth…
Multilinear PageRank
David F. Gleich, Lek-Heng Lim, Yongyang Yu
In this paper, we first extend the celebrated PageRank modification to a higher-order Markov chain. Although this system has attractive theoretical properties, it is computationall…
Computing active subspaces with Monte Carlo
Paul Constantine, David Gleich
Active subspaces can effectively reduce the dimension of high-dimensional parameter studies enabling otherwise infeasible experiments with expensive simulations. The key components…
Model Reduction with MapReduce-enabled Tall-and-Skinny Singular Value Decomposition
Paul G. Constantine, David F. Gleich, Yangyang Hou +1
We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the para…
Rank Aggregation via Nuclear Norm Minimization
David F. Gleich, Lek-Heng Lim
The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion…
The power and Arnoldi methods in an algebra of circulants
David F. Gleich, Chen Greif, James M. Varah
Circulant matrices play a central role in a recently proposed formulation of three-way data computations. In this setting, a three-way table corresponds to a matrix where each "sca…
Factorizing the Stochastic Galerkin System
Paul G. Constantine, David F. Gleich, Gianluca Iaccarino
Recent work has explored solver strategies for the linear system of equations arising from a spectral Galerkin approximation of the solution of PDEs with parameterized (or stochast…
Spectral Methods for Parameterized Matrix Equations
Paul G. Constantine, David F. Gleich, Gianluca Iaccarino
We apply polynomial approximation methods -- known in the numerical PDEs context as spectral methods -- to approximate the vector-valued function that satisfies a linear system of…