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URN: urn:nbn:de:0030-drops-20803
URL: http://drops.dagstuhl.de/opus/volltexte/2009/2080/
Daitch, Samuel I. ; Spielman, Daniel A.

A Nearly-Linear Time Algorithm for Approximately Solving Linear Systems in a Symmetric M-Matrix

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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:DSP:2009:2080,
  author =	{Samuel I. Daitch and Daniel A. Spielman},
  title =	{A Nearly-Linear Time Algorithm for Approximately Solving Linear Systems in a Symmetric M-Matrix},
  booktitle =	{Combinatorial Scientific Computing},
  year =	{2009},
  editor =	{Uwe Naumann and Olaf Schenk and Horst D. Simon and Sivan Toledo},
  number =	{09061},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2080},
  annote =	{Keywords: M-matrix, diagonally-dominant matrix, linear system solver, iterative algorithm, randomized algorithm, network flow, gain graph}
}

Keywords: M-matrix, diagonally-dominant matrix, linear system solver, iterative algorithm, randomized algorithm, network flow, gain graph
Seminar: 09061 - Combinatorial Scientific Computing
Issue date: 2009
Date of publication: 24.07.2009

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