License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.09061.3
URN: urn:nbn:de:0030-drops-20803
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/2080/
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Daitch, Samuel I. ;
Spielman, Daniel A.
A Nearly-Linear Time Algorithm for Approximately Solving Linear Systems in a Symmetric M-Matrix
Abstract
We present an algorithm for solving a linear system in a symmetric M-matrix.
In particular, for $n times n$ symmetric M-matrix $M$, we show how to find a diagonal matrix $D$ such that
$DMD$ is diagonally-dominant. To compute $D$, the algorithm must solve $O{log n}$ linear systems in diagonally-dominant matrices. If we solve these diagonally-dominant systems approximately using the Spielman-Teng
nearly-linear time solver, then we obtain an algorithm for approximately solving linear systems in symmetric M-matrices, for which the expected running time is also nearly-linear.
BibTeX - Entry
@InProceedings{daitch_et_al:DagSemProc.09061.3,
author = {Daitch, Samuel I. and Spielman, Daniel A.},
title = {{A Nearly-Linear Time Algorithm for Approximately Solving Linear Systems in a Symmetric M-Matrix}},
booktitle = {Combinatorial Scientific Computing},
pages = {1--4},
series = {Dagstuhl Seminar Proceedings (DagSemProc)},
ISSN = {1862-4405},
year = {2009},
volume = {9061},
editor = {Uwe Naumann and Olaf Schenk and Horst D. Simon and Sivan Toledo},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2009/2080},
URN = {urn:nbn:de:0030-drops-20803},
doi = {10.4230/DagSemProc.09061.3},
annote = {Keywords: M-matrix, diagonally-dominant matrix, linear system solver, iterative algorithm, randomized algorithm, network flow, gain graph}
}
Keywords: |
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M-matrix, diagonally-dominant matrix, linear system solver, iterative algorithm, randomized algorithm, network flow, gain graph |
Collection: |
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09061 - Combinatorial Scientific Computing |
Issue Date: |
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2009 |
Date of publication: |
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24.07.2009 |