@article{ef301ae766644b14ac3bf1a57aa0c433,
title = "“Compress and eliminate” solver for symmetric positive definite sparse matrices",
abstract = "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.",
keywords = "Direct solver, Hierarchical matrix, Sparse matrix, Symmetric positive definite matrix",
author = "Sushnikova, {Daria A.} and Oseledets, {Ivan V.}",
note = "Funding Information: ∗Submitted to the journal{\textquoteright}s Methods and Algorithms for Scientific Computing section March 30, 2016; accepted for publication (in revised form) February 16, 2018; published electronically June 14, 2018. http://www.siam.org/journals/sisc/40-3/M106848.html Funding: The work was supported by Russian Foundation of Basic Research grant 17-01-00854. †Skolkovo Institute of Science and Technology, Moscow, Russia (
[email protected]). ‡Skolkovo Institute of Science and Technology, Moscow, Russia, 143025 and Institute of Numerical Mathematics Russian Academy of Sciences, Moscow, Russia, 119333 (
[email protected]). Publisher Copyright: {\textcopyright} 2018 Society for Industrial and Applied Mathematics.",
year = "2018",
doi = "10.1137/16M1068487",
language = "English (US)",
volume = "40",
pages = "A1742--A1762",
journal = "SIAM Journal on Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}