8 citations · 31 across the 14 of their papers we have counts for
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Representing the Special Linear Group with Block Unitriangular Matrices
John Urschel
We prove that every element of the special linear group can be represented as the product of at most six block unitriangular matrices, and that there exist matrices for which six p…
Some New Results on the Maximum Growth Factor in Gaussian Elimination
Alan Edelman, John Urschel
This paper combines modern numerical computation with theoretical results to improve our understanding of the growth factor problem for Gaussian elimination. On the computational s…
Uniform Error Estimates for the Lanczos Method
John C. Urschel
The Lanczos method is one of the most powerful and fundamental techniques for solving an extremal symmetric eigenvalue problem. Convergence-based error estimates depend heavily on…
Constructing Frequency Domains on Graphs in Near-Linear Time
John C. Urschel, Wenfang Xu, Ludmil T. Zikatanov
Analysis of big data has become an increasingly relevant area of research, with data often represented on discrete networks both constructed and organic. While for structured domai…
On the Approximation of Laplacian Eigenvalues in Graph Disaggregation
Xiaozhe Hu, John C. Urschel, Ludmil T. Zikatanov
Graph disaggregation is a technique used to address the high cost of computation for power law graphs on parallel processors. The few high-degree vertices are broken into multiple…
On the Maximal Error of Spectral Approximation of Graph Bisection
John C. Urschel, Ludmil T. Zikatanov
Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a…
A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians
John C. Urschel, Xiaozhe Hu, Jinchao Xu +1
In this paper, we develop a cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smalle…