``Compress and Eliminate” Solver for Symmetric Positive Definite Sparse Matrices
Daria Sushnikova, Ivan Valer'evich Oseledets · SIAM Journal on Scientific Computing · 2018
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm applies hierarchically block Gaussian elimination and additionally compresses 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 the state-of-art direct and iterative solvers.