"Compress and eliminate" solver for symmetric positive definite sparse matrices
Numerical Analysis
2018-05-08 v4 Numerical Analysis
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.
Cite
@article{arxiv.1603.09133,
title = {"Compress and eliminate" solver for symmetric positive definite sparse matrices},
author = {Daria A. Sushnikova and Ivan V. Oseledets},
journal= {arXiv preprint arXiv:1603.09133},
year = {2018}
}