John Urschel, Raven's Offensive Lineman Publishes Math Paper

"John Urschel is an offensive lineman for the NFL Baltimore Ravens whose Twitter handle is @MathMeetsFball. He has bachelor's and master's degrees in math, both with a 4.0 grade-point average. And this week he tweeted:"

"My paper, A Cascadic Multigrid Algorithm for Computing the Fiedler Vector..., has been published in the Journal of Computational Mathematics."

"Now, journalists are notoriously poor at math (or at least this one is), so we'll provide a link to the paper. And for those of you who are mathematically inclined, here's the abstract:"

"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 smallest eigenvalue. This vector has been found to have applications in fields such as graph partitioning and graph drawing. The algorithm is a purely algebraic approach based on a heavy edge coarsening scheme and pointwise smoothing for refinement. To gain theoretical insight, we also consider the related cascadic multigrid method in the geometric setting for elliptic eigenvalue problems and show its uniform convergence under certain assumptions. Numerical tests are presented for computing the Fiedler vector of several practical graphs, and numerical results show the efficiency and optimality of our proposed cascadic multigrid algorithm."