On two-grid convergence estimates

We derive a new representation for the exact convergence factor of classical two‐level and two‐grid preconditioners. Based on this result, we establish necessary and sufficient conditions for constructing the components of efficient algebraic multigrid (AMG) methods. The relation of the sharp estima...

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Bibliographic Details
Published inNumerical linear algebra with applications Vol. 12; no. 5-6; pp. 471 - 494
Main Authors Falgout, Robert D., Vassilevski, Panayot S., Zikatanov, Ludmil T.
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.06.2005
Subjects
algebraic multigrid
convergence
sharp estimates
two-grid
two-level methods
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Summary:We derive a new representation for the exact convergence factor of classical two‐level and two‐grid preconditioners. Based on this result, we establish necessary and sufficient conditions for constructing the components of efficient algebraic multigrid (AMG) methods. The relation of the sharp estimate to the classical two‐level hierarchical basis methods is discussed as well. Lastly, as an application, we give an optimal two‐grid convergence proof of a purely algebraic ‘window’‐AMG method. Published in 2005 by John Wiley & Sons, Ltd.
Bibliography:The paper is dedicated to the 70th birthday of Owe Axelsson, a pioneer in two-level preconditioning methods
The work of the third author was supported in part by the National Science Foundation - No. DMS-0209497; No. SCREMS DMS-0215392
This article is a U.S. Government work and is in the public domain in the U.S.A.
ArticleID:NLA437
istex:F4AD2F379F1C4F0FF244CF41B3B4DFA41D226BD3
ark:/67375/WNG-32HQ17ST-F
U.S. Department of Energy - No. W-7405-Eng-48
The paper is dedicated to the 70th birthday of Owe Axelsson, a pioneer in two‐level preconditioning methods
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.437