# Approximate Gaussian Elimination for Laplacians - Fast, Sparse, and Simple

@article{Kyng2016ApproximateGE, title={Approximate Gaussian Elimination for Laplacians - Fast, Sparse, and Simple}, author={Rasmus Kyng and Sushant Sachdeva}, journal={2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)}, year={2016}, pages={573-582} }

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 the product of a sparse lower triangular matrix with its transpose. This gives 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. Our algorithm performs a subsampled Cholesky… CONTINUE READING

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