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arXiv · 1603.09133

"Compress and eliminate" solver for symmetric positive definite sparse matrices

Daria A. Sushnikova·Ivan V. Oseledets
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Abstract

We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in. The systems that have efficient compression of the fill-in mostly arise from discretization of partial differential equations. We show that the resulting factorization can be used as an efficient preconditioner and compare the proposed approach with state-of-art direct and iterative solvers.

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Daria A. Sushnikova, Ivan V. Oseledets. 2016-03-30. "Compress and eliminate" solver for symmetric positive definite sparse matrices. https://arxiv.org/abs/1603.09133

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