A&C Seminar: Approximate Gaussian Elimination for Laplacians

Wednesday, September 28, 2016 - 3:00pm to 4:00pm
Location: 
32-G575
Speaker: 
Rasmus Kyng
Biography: 
Yale
Abstract:We show how to perform sparse approximate Gaussian elimination for Laplacian matrices. We present a simple, nearly linear time algorithm that approximates a Laplacian by a matrix with a sparse Cholesky factorization – the version of Gaussian elimination for positive semi-definite matrices. We compute this factorization by subsampling standard Gaussian elimination. This is the first nearly linear time solver for Laplacian systems that is based purely on random sampling, and does not use any graph theoretic constructions such as low-stretch trees, sparsifiers, or expanders. The crux of our proof is the use of matrix martingales to analyze the algorithm.

Joint work with Sushant Sachdeva.