Approximate Gaussian Elimination for Laplacians: Fast, Sparse, and Simple
No Thumbnail Available
Author(s)
Kyng, Rasmus
Advisor(s)
Editor(s)
Collections
Supplementary to:
Permanent Link
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.
Sponsor
Date
2016-11-28
Extent
60:59 minutes
Resource Type
Moving Image
Resource Subtype
Lecture