# Sparsified Cholesky Solvers for SDD linear systems

@article{Lee2015SparsifiedCS, title={Sparsified Cholesky Solvers for SDD linear systems}, author={Yin Tat Lee and Richard Peng and Daniel A. Spielman}, journal={ArXiv}, year={2015}, volume={abs/1506.08204} }

We show that Laplacian and symmetric diagonally dominant (SDD) matrices can be well approximated by linear-sized sparse Cholesky factorizations. We show that these matrices have constant-factor approximations of the form $L L^{T}$, where $L$ is a lower-triangular matrix with a number of nonzero entries linear in its dimension. Furthermore linear systems in $L$ and $L^{T}$ can be solved in $O (n)$ work and $O(\log{n}\log^2\log{n})$ depth, where $n$ is the dimension of the matrix.
We present…

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