Video of this talk is available at: https://smartech.gatech.edu/handle/1853/56087Full collection of talk videos are available at: https://smartech.gatech.edu/handle/1853/46836
Algorithms & Randomness Center (ARC)
Monday, November 28, 2016
Klaus 1116 East - 11am
Approximate Gaussian Elimination for Laplacians: Fast, Sparse, and Simple
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.
Rasmus Kyng is a PhD student in Computer Science at Yale University, advised by Dan Spielman. Before attending Yale, he received a BA in Computer Science from the University of Cambridge in 2011. His research interests include graph algorithms, applied and theoretical machine learning, and linear systems.