Speaker: Chao Chen, Assistant Professor, Department of Mathematics, NCSU

Title: Efficient matrix computation for scientific computing and data analytics
Abstract:Matrix computations are ubiquitous in scientific computing and data science. However, many existing methods consume enormous computational resources for solving increasingly large and complex problems. In this talk, I will describe my work on exploiting mathematical structures and hardware capabilities to accelerate matrix computations. I will focus on a randomized algorithm, namely RChol, for computing an incomplete Cholesky factorization of a graph Laplacian, which arises from data clustering, semi-supervised learning, and the solution of partial differential equations. RChol employs a randomized sampling scheme developed by Spielman and Kyng to prevent excessive fill-in introduced by Gaussian elimination. I will prove the stability of RChol and show the extension to handle symmetric diagonally dominant matrices. Compared to its deterministic counterparts, RChol delivers faster convergence, less running time, and better parallel scalability.