EADS Talk by Rasmus Kyng: Approximate Gaussian Elimination for Laplacians – University of Copenhagen

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Department of Computer Science DIKU > Research > Algorithms and Programming Languages Section (APL) > EADS > Upcoming talks and events > EADS Talk by Rasmus Ky...

EADS Talk by Rasmus Kyng: Approximate Gaussian Elimination for Laplacians

Title

Approximate Gaussian Elimination for Laplacians

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.